angle addition postulate homework 5

Angle Addition Postulate: Explained with Examples

This lesson will give you the definition of the angle addition postulate, visual examples, and explanations and how it is used.

Angles can be found everywhere – the hands of a clock, wheels, pyramids and most importantly in design and construction of architecture, such as roads and buildings.

Once you’re confident in the basics of angles and how the postulate works, you will be able to work through the practice questions at the end of this lesson.

The Angle Addition Postulate: A Definition Actual Meaning: The Main Idea Real-Life Application Another Postulate: The Segment Addition Postulate Geometry Practice Questions Refresher: Parts of the Angle To Sum Up (Pun Intended!)

The Angle Addition Postulate: A Definition

The textbook definition goes a little like this:

If the point B lies in the interior of angle AOC then

Actual Meaning: The Main Idea

So, if you place two angles side by side, they are adjacent. Then the new angle made by both together is the sum of the two original angles.

You can picture this using two arrowheads.

The blue arrowhead has sides BL and UL, so the vertex is L. The tip of the arrow forms the angle ∠BLU which measures 40°.

The green arrowhead has sides GR and NR, so the vertex is R. These three points create ∠GRN which measures 60°.

By placing the two arrowheads side by side so that the points L and R join, and the points U and G join, a pair of adjacent angles has been made.

This has created a new angle measured from side B to N. This is angle ∠BRN.

By adding the two adjacent angles ∠GRN and ∠BLU together, you can find ∠BRN.

So in this case…

So, there you have it! The ∠BRN is 100°.

Here’s a fun tool to play around with and explore how changing the size of two adjacent angles affects the measure of the resulting angle.

You will find that changing points A, D, or C will affect the resulting angle it makes, without affecting the adjacent angle.

However— notice how the resulting angle changes? This is because it is the sum of the two adjacent angles.

Now you know how the postulate works, let’s work through an example and calculate the resulting angle.

As you can see these angles share the same side KL, so they are adjacent.

The angle ∠JKL is a right angle so it is 90°, and from the diagram, you will see LKM is 30°.

You can find their resulting angle as the sum of 90° and 30° so ∠JKM is 120°.

Real-Life Application: Angle Addition Postulate

Now you know how the postulate works, you must know how it can be used in real life.

There are many applications of the postulate, especially in architecture and engineering.

Roof trusses are beams of timber organized in triangles in the roofs of buildings.

It is important the angles in each triangle are measured correctly, as roof trusses provide support for a roof.

The Howe truss is made up of two 60° triangles and the Fink truss is made with three 40° triangles.

The same idea also applies to bridges. Some bridges have cables connected to bridges at angles from the bridge floor to towers.

These cables placed at specific angles support the bridge’s structure by sharing the weight of the bridge evenly across its supports.

Another Postulate: The Segment Addition

The Segment Addition Postulate is similar to the angle addition postulate, but you are working with line segments instead of adjacent angles.

If the point B is between A and C on a line segment, then:

To keep it simple, you can add connected line segments in the same way you can add adjacent angles!

Thank you to Lamee Storage for the video.

Here’s a worked example:

Use the postulate, substitute the values that we know, and do a little rearranging:

Now you have found x, substitute this into the formula for AB which is 2x.

Geometry Practice Questions

Please don’t try and use a protractor to find the angles. Not only will you miss out on the valuable practice, but you’ll get the answer wrong… because they’re not drawn accurately!

Using the postulate, form the equation

Angle ∠AOC is 74°.

Write out the postulate.

Using the fact that ∠DEF is a right angle, calculate the sum of the 3 adjacent angles.

The angle ∠JKM is straight, so the two adjacent angles sum to 180°.

Angle ∠MOP is a right angle, so the two adjacent angles add up to 90°.

To find ∠MON subtract ∠NOP from 90°.

The sum of angle ∠RQS and ∠SQT is equal to 136°.

The sum of these adjacent angles

Solve for x using the size of ∠RQT.

Find the sum of ∠VUW and ∠WUX to find the angle ∠VUX.

∠WUX is a right angle so it is 90° and ∠VUW is 48° so their sum is 138°.

Solve this with the equation for ∠VUX.

Form the equation using the postulate.

The sum of the two adjacent angles is:

From the question, you know the angle ∠XWZ is 95 so:

Angle ∠BAD is a straight line so it is 180°.

Using the formula ∠BAD=∠BAC+∠CAD, you can solve:

Then find x.

Substitute this value of x into the equation for ∠CAD.

Using the formula:

Find the sum of the two adjacent angles.

Using the equation given for ∠EFH:

Substitute this value of x into the equation for ∠EFH.

∠DAE is a right angle, so it is 90°.

BE is a straight line, so ∠BAE is 180°. This means ∠BAC, ∠CAD, and ∠DAE sum to 180°.

Rearrange and solve for x.

Parts of The Angle: A Brief Refresher

An angle is formed when two lines or rays meet at the same endpoint.

The symbol ∠ can be used to represent angles. The angle below is written ∠ABC.

Angles are usually measured in degrees , which are represented by the symbol °. We would write the name and size of the angle above like this:

BA and BC are the sides of the angle, also known as rays .

B is the common vertex – the point they share between the sides BA and BC.

Important: when naming an angle, the middle letter must be the common vertex.

The interior angle is the angle between the two sides, whereas the exterior angle is the angle outside of the two sides.

The last definition you need before moving on is for adjacent angles , which share a side and a vertex.

Here is an example:

See how the angles share the vertex, O, and the line in the middle, OB.

The angle x can be shown as ∠AOB.

Angle y is ∠BOC or ∠COB

Angle z is ∠AOC or ∠COA.

As you can see, it doesn’t matter which order you put the letters in, as long as the common vertex is in the middle, “O” in the case above.

To Sum Up (Pun Intended!)

By making two angles adjacent, you can find their resulting angle by adding the two original angles.

This can be applied similarly to finding the sums of line segment lenghts.

You also saw how to define and recognize adjacent angles, which is important in applying the angle addition postulate.

For more help and lessons, head to the homepage .

For now, hopefully, you feel confident in finding the total of adjacent angles. Post your answers to any of the challenges or leave any questions in the comments below!

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Calcworkshop

Angle Addition Postulate Defined w/ 29+ Brilliant Examples!

// Last Updated: January 21, 2020 - Watch Video //

Today you’re going to learn all about angles, more specifically the angle addition postulate.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

We’re going to review the basics of angles, and then use that knowledge to find missing angles with our new postulates.

Let’s dive in!

How To Name An Angle?

The first thing you need to know about angles is how to identify or name them.

For example, did you know that an angle is formed by two rays that have the same common endpoint or initial point?

And that the common endpoint is called the vertex of the angle.

Parts of an Angle

To name the angle we typically use three points when naming an angle, one point on each side and also the vertex. It is important to note that the vertex must always be the middle letter.

The angle seen below can be named ∠NPM or ∠MPN

Naming an Angle

Angle Classifications

And angles are classified as to their measure and are labeled as either acute angles, right angles, obtuse angles, or straight angles.

Angle Classification

Did you know that there is something amazing about adjacent angles?

First, adjacent angles are two angles that have a common vertex and side but no common interior points. Meaning, they are two angles side-by-side with the same vertex.

Adjacent Angles Examples

But the most significant thing about adjacent angles is that we can add their measures to create larger angles.

By using the Angle Addition Postulate!

Angle Addition Postulate

The postulate states that if we have two adjacent angles, we can add their measures to help us find unknown angles.

Angle Addition Postulate Definition

As seen in the example to the right, ∠ACB + ∠CDB = ∠ADC

Angle Addition Postulate Example

And finally, just like we saw with segments, angles also have bisectors.

We discuss this in detail in the video below, but essentially an angle bisector is a ray from the vertex of an angle that forms two congruent angles from the given angle.

In other words, it divides the angle in half, or cuts it into two equal parts, as Math is Fun accurately states.

Angle Bisector

Together we will learn how to:

• Identify and classify angles.
• Understand adjacent angles.
• Use the angle addition postulate to find angle measures.
• Recognize an angle bisector.
• Identify congruent angles.

Angles and Their Measures – Lesson & Examples (Video)

• Introduction to angles.
• 00:00:16 – What is an angle?
• 00:07:28 – Understanding adjacent angles and how to classify angles (Examples #1-4)
• 00:16:34 – What is the angle addition postulate (Examples #5-7)
• Exclusive Content for Member’s Only
• 00:28:11 – Find the measure of each angle and classify the angle (Examples #8-20)
• 00:39:53 – What is an angle bisector? (Examples #21-23)
• 00:45:32 – Find the measure of each angle given an angle bisector (Examples #24-25)
• 00:53:29 – Tell whether each statement is always, sometimes or never true (Examples #26-30)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Angle Addition Postulate

The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle. For example, if ∠AOB and ∠BOC are adjacent angles on a common vertex O sharing OB as the common arm, then according to the angle addition postulate, we have ∠AOB + ∠BOC = ∠AOC.

Angle Addition Postulate Definition

The definition of angle addition postulate states that "If a ray is drawn from point O to point P which lies in the interior region of ∠MON, then ∠MOP + ∠NOP = ∠MON". This postulate can be applied to any pair of adjacent angles in math. In other words, the angle addition postulate can be defined as 'the sum of two angles joined together through a common arm and a common vertex is equal to the sum of the resulting angle formed'.

Angle Addition Postulate Formula

If an angle AOC is given where O is the vertex joining rays OA and OC, and there lies a point B in the interior of ∠AOC, then the angle addition postulate formula is given as ∠AOB+∠BOC = ∠AOC. If ∠AOC is divided into more than two angles such as ∠AOB, ∠BOD, and ∠DOC, then also we can apply the formula of angle addition postulate as ∠AOB+∠BOD+∠DOC = ∠AOC.

Topics Related to Angle Addition Postulate:

Check these interesting articles related to the concept of angle addition postulate in math.

• Segment Addition Postulate
• Angle Addition Postulate Worksheets
• Angle Sum Theorem

Angle Addition Postulate Examples

Example 1: In the figure given below, if ∠POS is a right angle, ∠2 = 30°, and ∠3 = 40°. Find the value of ∠1.

Solution: It is given that ∠POS is a right angle. It means that ∠POS = 90°. Now, by using the angle addition postulate formula, we can write ∠1 + ∠2 + ∠3 = 90°. Given, ∠2 = 30° and ∠3 = 40°. Substituting these values in the above equation, we get,

∠1 + 30° + 40° = 90°

∠1 + 70° = 90°

∠1 = 90° - 70°

Therefore, the value of ∠1 is 20°.

Example 2: In the given figure, XYZ is a straight line. Find the value of x using the angle addition postulate.

Solution: It is given that XYZ is a straight line. It means that ∠XYO and ∠OYZ form a linear pair of angles.

⇒ ∠XYO + ∠OYZ = 180° (using angle addition postulate and linear pair of angles property)

⇒ (3x + 5) + (2x - 5) = 180°

⇒ 5x = 180°

Therefore, the value of x is 36.

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Practice Questions on Angle Addition Postulate

Faqs on angle addition postulate, what is angle addition postulate in geometry.

The angle addition postulate in geometry is a mathematical axiom which states that if there is a ray drawn from O to Q which is any point inside the region of angle POR, then the sum of angles ∠POQ and ∠QOR is equal to ∠POR. It can be represented in the form of a mathematical equation as ∠POQ + ∠QOR = ∠POR.

What is the Angle Addition Postulate Formula?

The formula of angle addition postulate in math is used to express the sum of two adjacent angles. If there are two angles (∠AOB and ∠BOC) joined together sharing a common arm OB and a common vertex O, then the angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC.

How to Find x in Angle Addition Postulate?

If there is any missing angle 'x' when two or more angles are joined together, then we can subtract the sum of remaining angles from the total sum to find the value of x. For example, if two angles ∠PQR and ∠RQS are joined together such that ∠RQS = 40°, ∠PQR = x, and ∠PQS = 70°, then the value of x will be (70 - 40)° = 30°.

How to Use Angle Addition Postulate?

The angle addition postulate can be used to find the sum of two or more adjacent angles and to find the missing values of angles. It establishes a relation between the measurement of angles joined together.

How do you Find the Angle Addition Postulate?

The angle addition postulate is a mathematical fact that can be considered true without any proof. It tells us that the sum of two or more angles joined together is equal to the sum of the larger angle formed.

How is the Angle Addition Postulate Used in Real Life?

In real life, the angle addition postulate is used in construction (bridges, buildings, etc), architecture, designing, etc.

Angle Addition Postulate

Related Topics: More Lessons for High School Regents Exam Math Worksheets

High School Math based on the topics required for the Regents Exam conducted by NYSED.

Angle Addition Postulate The angle addition postulate states that if D is in the interior of ∠ABC then ∠ABD + ∠CBD = ∠ ABC

The following diagram gives an example of the Angle Addition Postulate. Scroll down the page for more examples and solutions.

Angle Addition Postulate and Angle Bisectors

• How to use the Angle Addition Postulate to find unknown angle measures.
• How to use angle bisectors to find unknown angle measures.

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Unit 1 Geometry Basics Homework 5 Angle Addition Postulate

Unit 1 Geometry Basics Homework 5 Angle Addition Postulate - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are The segment addition postulate date period, 2 the angle addition postulate, Basic geometry unit 1 post test answers pdf, Unit 1 tools of geometry reasoning and proof, 1 introductionto basicgeometry, Geometry unit answer key, Identify points lines and planes, Geometry notes chapter 1 essentials of geometry.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. The Segment Addition Postulate Date Period

2. 2-the angle addition postulate, 3. basic geometry unit 1 post test answers pdf, 4. unit 1: tools of geometry / reasoning and proof, 5. 1 introductionto basicgeometry, 6. geometry unit answer key, 7. 1.1 identify points, lines, and planes, 8. geometry notes chapter 1: essentials of geometry.

Angle Properties, Postulates, and Theorems

In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems. A postulate is a proposition that has not been proven true, but is considered to be true on the basis for mathematical reasoning. Theorems , on the other hand, are statements that have been proven to be true with the use of other theorems or statements. While some postulates and theorems have been introduced in the previous sections, others are new to our study of geometry. We will apply these properties, postulates, and theorems to help drive our mathematical proofs in a very logical, reason-based way.

Before we begin, we must introduce the concept of congruency. Angles are congruent if their measures, in degrees, are equal. Note : “congruent” does not mean “equal.” While they seem quite similar, congruent angles do not have to point in the same direction. The only way to get equal angles is by piling two angles of equal measure on top of each other.

We will utilize the following properties to help us reason through several geometric proofs.

Reflexive Property

A quantity is equal to itself.

Symmetric Property

If A = B , then B = A .

Transitive Property

If A = B and B = C , then A = C .

Addition Property of Equality

If A = B , then A + C = B + C .

Angle Postulates

Angle addition postulate.

If a point lies on the interior of an angle, that angle is the sum of two smaller angles with legs that go through the given point.

Consider the figure below in which point T lies on the interior of ?QRS . By this postulate, we have that ?QRS = ?QRT + ?TRS . We have actually applied this postulate when we practiced finding the complements and supplements of angles in the previous section.

Corresponding Angles Postulate

If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent.

Converse also true : If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.

The figure above yields four pairs of corresponding angles.

Parallel Postulate

Given a line and a point not on that line, there exists a unique line through the point parallel to the given line.

The parallel postulate is what sets Euclidean geometry apart from non-Euclidean geometry .

There are an infinite number of lines that pass through point E , but only the red line runs parallel to line CD . Any other line through E will eventually intersect line CD .

Angle Theorems

Alternate exterior angles theorem.

If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

Converse also true : If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.

The alternate exterior angles have the same degree measures because the lines are parallel to each other.

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then the alternate interior angles are congruent.

Converse also true : If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel.

The alternate interior angles have the same degree measures because the lines are parallel to each other.

Congruent Complements Theorem

If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.

Congruent Supplements Theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

Right Angles Theorem

All right angles are congruent.

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary.

Converse also true : If a transversal intersects two lines and the interior angles on the same side of the transversal are supplementary, then the lines are parallel.

The sum of the degree measures of the same-side interior angles is 180°.

Vertical Angles Theorem

If two angles are vertical angles, then they have equal measures.

The vertical angles have equal degree measures. There are two pairs of vertical angles.

(1) Given: m?DGH = 131

Find: m?GHK

First, we must rely on the information we are given to begin our proof. In this exercise, we note that the measure of ?DGH is 131° .

From the illustration provided, we also see that lines DJ and EK are parallel to each other. Therefore, we can utilize some of the angle theorems above in order to find the measure of ?GHK .

We realize that there exists a relationship between ?DGH and ?EHI : they are corresponding angles. Thus, we can utilize the Corresponding Angles Postulate to determine that ?DGH??EHI .

Directly opposite from ?EHI is ?GHK . Since they are vertical angles, we can use the Vertical Angles Theorem , to see that ?EHI??GHK .

Now, by transitivity , we have that ?DGH??GHK .

Congruent angles have equal degree measures, so the measure of ?DGH is equal to the measure of ?GHK .

Finally, we use substitution to conclude that the measure of ?GHK is 131° . This argument is organized in two-column proof form below.

(2) Given: m?1 = m?3

Prove: m?PTR = m?STQ

We begin our proof with the fact that the measures of ?1 and ?3 are equal.

In our second step, we use the Reflexive Property to show that ?2 is equal to itself.

Though trivial, the previous step was necessary because it set us up to use the Addition Property of Equality by showing that adding the measure of ?2 to two equal angles preserves equality.

Then, by the Angle Addition Postulate we see that ?PTR is the sum of ?1 and ?2 , whereas ?STQ is the sum of ?3 and ?2 .

Ultimately, through substitution , it is clear that the measures of ?PTR and ?STQ are equal. The two-column proof for this exercise is shown below.

(3) Given: m?DCJ = 71 , m?GFJ = 46

Prove: m?AJH = 117

We are given the measure of ?DCJ and ?GFJ to begin the exercise. Also, notice that the three lines that run horizontally in the illustration are parallel to each other. The diagram also shows us that the final steps of our proof may require us to add up the two angles that compose ?AJH .

We find that there exists a relationship between ?DCJ and ?AJI : they are alternate interior angles. Thus, we can use the Alternate Interior Angles Theorem to claim that they are congruent to each other.

By the definition of congruence , their angles have the same measures, so they are equal.

Now, we substitute the measure of ?DCJ with 71 since we were given that quantity. This tells us that ?AJI is also 71° .

Since ?GFJ and ?HJI are also alternate interior angles, we claim congruence between them by the Alternate Interior Angles Theorem .

The definition of congruent angles once again proves that the angles have equal measures. Since we knew the measure of ?GFJ , we just substitute to show that 46 is the degree measure of ?HJI .

As predicted above, we can use the Angle Addition Postulate to get the sum of ?AJI and ?HJI since they compose ?AJH . Ultimately, we see that the sum of these two angles gives us 117° . The two-column proof for this exercise is shown below.

(4) Given: m?1 = 4x + 9 , m?2 = 7(x + 4)

In this exercise, we are not given specific degree measures for the angles shown. Rather, we must use some algebra to help us determine the measure of ?3 . As always, we begin with the information given in the problem. In this case, we are given equations for the measures of ?1 and ?2 . Also, we note that there exists two pairs of parallel lines in the diagram.

By the Same-Side Interior Angles Theorem , we know that that sum of ?1 and ?2 is 180 because they are supplementary.

After substituting these angles by the measures given to us and simplifying, we have 11x + 37 = 180 . In order to solve for x , we first subtract both sides of the equation by 37 , and then divide both sides by 11 .

Once we have determined that the value of x is 13 , we plug it back in to the equation for the measure of ?2 with the intention of eventually using the Corresponding Angles Postulate . Plugging 13 in for x gives us a measure of 119 for ?2 .

Finally, we conclude that ?3 must have this degree measure as well since ?2 and ?3 are congruent . The two-column proof that shows this argument is shown below.

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Worksheets: The Angle Addition Postulate

• Geometry >
• Angles >
• Adjacent >
• Addition Postulate

One of the important properties of adjacent angles is that they can be added to give the measure of the angle that encloses them. The postulate which governs this process of addition is called the angle addition postulate. These printable worksheets containing six questions are intended to reinforce this postulate among the students and homeschoolers. Each question presents a pair of adjacent angles for practice. Add or subtract the given measures to find the measures of the indicated angles.

These pdf worksheets are ideal for grade 7 and grade 8 children.

Related Printable Worksheets

▶ Linear Pair of Angles

▶ Vertical Angles

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Angle Addition Postulate Homework 5

Displaying top 8 worksheets found for - Angle Addition Postulate Homework 5 .

Some of the worksheets for this concept are 2 the angle addition postulate, Geometry segment addition postulate work answer key, Angle addition postulate work all things algebra, Unit 1, Geometry basics segment addition postulate work, Segment addition postulate work answers, Unit 1 work using the angle addition postulate, Points lines planes angles.

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1. 2-The Angle Addition Postulate -

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Ms. Tecce's Math Classes: 2018 Honors Geometry

• 2019-2020 AP Statistics
• 2019-2020 Statistics & Probability
• 2019-2020 Geometry Concepts
• Salem Election Info for March 2021

Honors Geometry

Announcements

Due Wed, 1/16

Finish the 7 assigned Khan Academy problems

Upcoming Assessments:

Unit 7 Test Thurs, 1/10

Final Exam Wed, 1/23

Completed Reference Sheets

• HG Objects in Geometry Ref Sheet
• HG Vocabulary for Points, Lines, and Planes Ref Sheet
• HG Conditional Statements Ref Sheet
• HG Segments Ref Sheet
• HG Angles Ref Sheet
• HG Angle Relationships Ref Sheet
• HG Triangle Theorems Ref Sheet
• HG Circle Theorems Ref Shet
• HG Reasons #1 Algebraic Properties
• HG Reasons #2 Segments
• HG Reasons #3 Angles
• HG Reasons #4 Angles
• HG Reasons #5 Parallel Lines
• HG Reasons #7 Congruent Triangles

HG Unit 7 - Transformations, Congruent Triangles, and Special Quadrilaterals

Topics for Unit 7 - Transformations, Congruent Triangles, and Special Quadrilaterals

• Construct the image of a figure after a transformation using a compass, protractor, and/or ruler
• Plot the image of a figure after a transformation on a coordinate plane
• Describe a transformation in words and using coordinate notation
• Classify a transformation as an isometry
• Prove that triangles are congruent (SSS, ASA, SAS, AAS)
• Identify congruent parts of congruent triangles
• Write proofs involving congruent triangles
• Use the properties of parallelograms, rectangles, rhombuses, squares, trapezoids, and isosceles trapezoids to solve problems
• Classify a quadrilateral as a parallelogram, rectangle, rhombus, square, trapezoid, and/or isosceles trapezoid
• Apply the properties of a median of a trapezoid to solve problems
• Complete proofs involving parallelograms, rectangles, rhombuses, squares, trapezoids, and isosceles trapezoids (and congruent triangles)

Exercises in the book (all odd answers are in the back of the book):

p.501 #1-28, 36, 37            p.506 #1-17, 24-30                    p.513 #1-2, 6-9, 15, 31                     p.529 #6-8, 16-19, 26-31

p.329 #1-33, 39-44            p.337 #1-17, 20-36                p.344 #1-32, 35 

p.351 #1-8, 11-22, 30-35    p.359 #1, 3-9, 13-22, 25-26    p.370 #12-25

• HG Congruent Triangles Reference Sheet
• HG Congruent Triangles Proof Packet
• HG Congruent Triangles Proof Packet Answers (Flow proof)
• HG Congruent Triangle Proof Answers (2-column proofs)
• HG Quadrilaterals Reference Sheet
• HG Parallelogram Packet (plus more)

HG Unit 6 - Similarity & Trigonometry

Topics in Unit 6 - Similarity & Trigonometry

• Solve a proportion
• Write a ratio
• Use an extended ratio (a:b:c) to solve a problem
• Use the proportionality theorems to find missing lengths
• Determine whether two polygons are similar (check all corresponding angles are congruent and all corresponding sides are in the same ratio)
• Use similar polygons to find missing side lengths and angle measures
• Write a similarity statement for similar polygons
• Prove triangles similar (AA~, SAS~, SSS~)
• Write a proof to show triangles are similar (AA~)
• Find the scale factor for two similar polygons (and ratio of perimeters)
• Find missing side lengths of 45-45-90 triangles
• Find missing side lengths of 30-60-90 triangles
• Write trigonometric ratios
• Use trigonometry to find missing side lengths and angle measures of right triangles
• Solve word problems with trigonometry
• HG Practice Solving Proportions Answers
• HG Practice with Similar Triangles Answers
• HG Special Right Triangle Practice Answers
• HG Proving Triangles Similar Extra Practice Answers

HG Unit 5 - Circles

Topics in Unit 5 - Circles

• Identify parts of a circle (center, radius, chord, diameter, secant, tangent)
• Name a circle
• Find the circumference of a circle
• Find the area of a circle
• Find central angle and arc measures in a circle
• Find arc length and sector area
• Write the equation of a circle given a graph and/or points
• Graph a circle on a coordinate plane
• Use theorems to find missing lengths in and around a circle
• Use theorems to find angle measures
• Use theorems to find arc measures
• Use Pythagorean Theorem to find missing side lengths in a right triangle
• Use Converse of Pythagorean Theorem to classify a triangle as right, obtuse, or acute based on side lengths
• Find the midpoint, slope, and distance between two points on a coordinate plane

*All bold topics have already been covered in class.

Exercises in the Book (all odd answers are in the back of the book):

p.557 #1-52         p.567 #1-28, 32-47        p .574 #1-39                     p.583 #1-36        

p.593 #1-22         p.602 #1-26                     p.610 #1-15, 17-24         p.617 #2-32

• HG Unit 5 Review Packet
• HG Unit 5 Review Packet Answers

HG Unit 4 - Triangles

Topics in Unit 4 - Triangles

• Name a triangle and its parts (vertices, sides, interior angles)
• Classify a triangle by its angles (acute, right, obtuse, equiangular) and sides (scalene, isosceles, equilateral)
• Find unknown side lengths and angle measures based on a marked triangle
• Find unknown angle measures of a triangle (interior angles and exterior angles)
• Name a polygon by its number of sides/angles/vertices
• Use vocabulary including exterior angle, interior angle, remote interior angles, vertex angle, base angles, legs, and base)
• Understand and apply the Isosceles Triangle Theorem (and converse) to find missing angle and side measures of an isosceles triangle
• Prove that a triangle is isosceles
• Understand and apply the fact that an equilateral triangle is equiangular (and converse)
• Order the sides and/or angles of a triangle from least to greatest
• Determine whether a given set of side lengths can create a triangle
• Determine the range of possible side lengths for the third side of a triangle given the other two
• Understand and apply the Hinge Theorem to compare the side/angle measures of two triangles
• Construct the perpendicular bisector and angle bisectors of a triangle
• Understand and apply the Angle Bisector Theorem and Perpendicular Bisector Theorem to find missing measure
• Find unknown interior and exterior angle measures of convex polygons 
• Use vocabulary including convex, concave, and regular in reference to polygons

**Bold topics have already been covered in class

• HG Unit 4 Review Packet
• HG Unit 4 Review Questions Answers
• HG Extra Unit 4 Questions (with answers)

HG Unit 3 - Angles

Topics in Unit 3 - Angles

• Use vocabulary including ray, angle, vertex, congruent, bisect, and perpendicular
• Name and/or draw a ray
• Find the measure of an angle using a protractor
• Identify the vertex and sides of an angle and name the angle three different ways
• Determine the location of a point with respect to an angle (interior, exterior, or on an angle)
• Classify an angle as acute, obtuse, right, or straight
• Understand and apply the Angle Addition Postulate
• Use algebra to find missing measures of angles
• Identify and use angle relationships including vertical angles, linear pair, adjacent angles, congruent angles, complementary angles, and supplementary angles
• Prove facts involving Angle Addition Postulate, angle bisector, and other basic angle relationships
• Identify and use angle relationships including corresponding angles, alternate exterior angles, alternate interior angles, same-side interior angles, transversal, parallel lines, skew lines, and intersecting lines
• Construct angle bisectors, congruent angles, and parallel lines
• Prove facts involving angles and parallel lines

**All bold topics have already been covered in class

p.35 #1-36, 39, 45;   p.45 #1-22;    p.129 #1-15      p.145 #12-19, 24-35, 41-47       p.152 #1-30         p.175 #1-20, 23-26

• HG Objects in Geoemtry Reference Sheet
• HG Angles Reference Sheet
• HG Warm-up with Angle Measures
• HG Warm-up with Angle Measures Answers
• HG Practice with Bisectors, Complements, and Supplements Answers
• HG Angle Relationships Reference Sheet
• HG 3.2 Parallel Lines and Transversals Practice
• HG 3.2 Parallel Lines and Transversals Answers
• HG Big Angle Diagram Practice
• HG Big Angle Diagram Answers
• HG Unit 3 Review Problems
• HG Unit 3 Review Answers
• HG Unit 3 Angle Proof Practice Packet
• HG Unit 3 Angle Proof Practice Answers

HG Unit 2 - Segments

Topics in Unit 2 - Segments

• Name a segment
• Use vocabulary including line segment, endpoints, midpoint, between, congruent, bisect, and equidistant
• Find the measure of a segment using a ruler (in, cm, mm) and a grid
• Understand and apply the Segment Addition Postulate
• Use algebra to find missing measures of segments
• Use the midpoint formula to find the midpoint of points on a number line and/or coordinate plane
• Use the midpoint formula to find the missing endpoint given an endpoint and the midpoint
• Write a proof to prove facts involving line segments
• Find the perimeter of a polygon or composite figure
• Find the distance between a point and a line
• Use a compass and straight-edge to construct a segment bisector and model Segment Addition Postulate

Exercises in Book: (all odd answers are in the back of the book)

p.17 #1-3, 7-15, 22-39, 52, 53; p.25 #1-3, 5, 16, 29-50, 58, 59, 64-77; p.114 #1-4, 20; p.121 #1-3, 6-10, 16, 23-26

Assignments from this Unit:

• HG Adding Fractions Practice
• HG Practice with Segment Measures
• HG Practice with Segment Measures Answers
• HG Practice with Segments and Equations
• HG Practice with Segments and Equations Answers
• HG Midpoint Practice
• HG Midpoint Practice Answers
• HG Warm-up with Models
• HG Warm-up with Models Answers
• HG Segment Equations and Midpoints QC Answers
• HG Segment Jigsaw Proof Questions
• HG Segment Jigsaw Puzzle Answers
• HG Proving Segment Relationships Practice
• HG Proving Segment Relationships Practice Answers
• HG Extra Segment Proof Practice
• HG Extra Segment Proof Practice Answers
• HG Unit 2 Review Packet
• HG Unit 2 Review Answers

HG Unit 1 - Basics of Geometry

Topics in Unit 1: Basics of Geometry

• Name points, lines, and planes
• Model situations involving points, lines, and planes
• Use vocabulary including collinear, noncollinear, coplanar, conjecture , intersect, parallel, between, and perpendicular
• Make a conjecture about the next item in a sequence.
• Write a conditional statement in if-then form and identify the hypothesis and conclusion
• Write the converse, inverse, and contrapositive of a conditional statement
• Determine if a conjecture if true or false (and provide a counterexample if false)
• Recognize Reflexive, Symmetric, and Transitive properties
• Complete an Algebraic Proof (citing the "Reasons")

**All bold concepts have already been covered in class.

Assignments:

Due 8/31: Add yourself to the Google Classroom and submit answers to the posted questions ... Class Code:  v48omk

Due 9/5: Complete "Points and Lines Practice" and "Intersecting Planes Activity"

Due 9/7: Submit definitions for each of the related conditional statements through the Google Classroom

Due 9/12: Complete the "Practice with Algebraic Properties" and "Unit 1 Review Packet"

Extra Textbook Questions for Unit 1: (all odd answers are in the back of the textbook)

p.9 #1-34;  p.80 #1-2, 4, 7-18, 26, 27, 29, 31-35, 37, 38;  p.88 #25-31, 42-47; p.94 #1-47, 49, 70-72; p.101 #3-5, 9-12, 17, 21, 25, 26;  p.108 #17-20;  p.114 #1, 2, 4, 6, 8-20, 22-26, 36-42

• HG Points and Lines Practice
• HG Points, Lines, and Planes Practice
• HG Points, Lines, and Planes Practice Answers
• HG Warm-up #1 with Hearts
• HG Warm-up #1 with Hearts Answers
• HG Inductive Reasoning Practice
• HG Inductive Reasoning Practice Answers *#3 should say -192
• HG Conditional Statements Practice
• HG Conditional Statements Practice Answers
• HG Practice with Deductive Reasoning
• HG Practice with Deductive Reasoning Answers
• HG Practice with Algebraic Properties
• HG Practice with Algebraic Properties Answers
• HG Unit 1 Review Questions
• HG Unit 1 Review Questions Answers
• HG More Algebraic Proof Practice (with Answers) Difficult proof questions like today's class
• HG Unit 1 Test from 2017
• HG Unit 1 Test from 2017 Answers

Course Information

• Honors Geometry Course Expectations
• Classroom Rules
• Last Updated: Feb 8, 2021 2:44 PM
• URL: https://sau57.org/tecce