Interactive PowerPoint Study Guide for Unit Test 1

UNIT 1 REVIEW

Click HERE to go to the topics.

CLICK TO EXPLORE UNIT 1

Unit 1 Objective

s

Naming and

Classifying

Divided Line

Segments

Divided Angles

Angle Relationship

sTriangles

Isosceles and

Equilateral

Properties

For SAT Practice, look on the CCSC website for the SAT PowerPoint from class.

For justification practice, look over notes, classwork, and homework.

You will be held responsible for everything in the Unit 1 Objectives. For topics not in this PowerPoint, look over notes, classwork, homework, do-

nows, and exit tickets.

name points, lines, line segments, rays, planes, angles, and triangles using names of points.

identify whether a set of given points is collinear. identify acute, obtuse, right, and straight angles

given a diagram or measurementsolve problems about congruent segments and

divided or bisected line segments.solve problems about congruent angles and divided

or bisected angles.solve problems about angle relationships, including

vertical and straight angles.use the fact that angles in a circle add up to 360 to

solve problems.determine the measurement of an angle that is

complementary or supplementary to a given angle.

YOU SHOULD BE ABLE TO…

There’s more!

determine the measurement of an angle that is complementary or supplementary to a given angle

use the triangle sum theorem to solve problems.Use the exterior angle theorem to solve problemsuse properties of angles in isosceles and equilateral

triangles to solve problems. use the “draw a picture and write in everything you

know” strategy to solve problems about angles in triangles.

write logical justifications to solutions to geometry problems using the following phrases “it is given that…” “Because [property]…” “Hence,…” and “Therefore [conclusion]”

solve SAT-type problems involving lines, angles, and triangles.

YOU SHOULD BE ABLE TO…

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NAMING AND CLASSIFYING OVERVIEW

Click each box to see the label and sketch for each geometric figure.

Point Line Line Segment

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NAMING AND CLASSIFYING OVERVIEW

Click each box to see the label and drawing for each geometric figure.

Ray Angle Triangle

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*careful to label rays starting with the initial point.

*you should only label angles using one point if there are no other angles sharing the same vertex. Otherwise, use 3 points to label.

CLASSIFYING ANGLES

Click each box to see the definition and examples of each type of angle.

Acute Right

Obtuse Straight

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Try some Example

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Angles that are greater than but less than

Angles that are equal to

Angles that are greater than but less than

Angles that are equal to

Use the figure shown to answer the problems.

CLASSIFYING EXAMPLES

1. List all of the angles that have S as a vertex.

2. Name a straight angle.

3. Name an obtuse angle.

4. Does appear to be obtuse, straight, right, or acute?

1. Show Answer

2. Show Answer

3. Show Answer

4. Show Answer

∠𝑇𝑆𝑈 ,∠𝑅𝑆𝑈 ,𝑎𝑛𝑑∠𝑅𝑆𝑇

∠𝑅𝑆𝑇

∠𝑇𝑆𝑈

Acute

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More Example

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Name three collinear points shown in the diagram below.

CLASSIFYING EXAMPLES

Collinear Points:

Points that lie on the same line.

Show Answer

A, E, and Cor

D, E, and B

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Click each box to learn the vocabulary.

DIVIDED LINE SEGMENTS

congruent segments

bisects midpoint

two segments that have the same length.

divides a segment into two congruent segments

a point that bisects a segment

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DIVIDED LINE SEGMENTS

The Segment Addition Postulate:

If point B is between A and C, then AB+BC=AC.

Also,if AB+BC=AC, then point B is between A and C. AB + BC

= AC

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Try Some

Examples

If and , what is the length of ?

If and , what is the length of ?

DIVIDED SEGMENTS EXAMPLES

Note: Not drawn to scale.

Use the figure below to answer the questions.

Show Answer 𝐴𝐶=24

Show Answer 𝐵𝐶=16

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More Example

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If , and , find .

If is two more than three times the length of and is 26, what is the length of ?

DIVIDED SEGMENTS EXAMPLES

Note: Not drawn to scale.

Use the figure below to answer the questions.

Show Answer 𝑥=16

Show Answer 𝐴𝐵=16

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More Example

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is the midpoint of . If and , what is the length of

In parallelogram bisects and . If and what is the value of ?

DIVIDED SEGMENTS EXAMPLES

Show Answer 𝑋𝑍=4

Show Answer 𝑦=12

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DIVIDED ANGLES

Click each box to learn the vocabulary.

congruent angles

bisects bisector

two angles that have the same measure.

divides an angle into two congruent angles

a ray or segment that bisects an angle

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DIVIDED ANGLES

The Angle Addition Postulate:

If ray is on the interior of then .

Also,if then ray is on the interior of .

∠𝐴𝐵𝐷+¿

∠𝐷𝐵𝐶

¿∠𝐴𝐵𝐶Return to Main

Try Some

Examples

DIVIDED ANGLES EXAMPLES

Show Answer

𝑥=36

Show Answer

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More Example

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bisects If and then find the values of and the measure of all three angles ( and )

[Figure not drawn to scale]

DIVIDED ANGLES EXAMPLES

Show Answer ,

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ANGLE RELATIONSHIPS

Click each box to see the definition and examples of each angle relationship.

Vertical Angles Linear Pairs

Complementary Angles

Supplementary Angles

Angles that share a vertex and are formed by two pairs of opposite rays.*All vertical angles are congruent*

Two angles that share an adjacent side and whose other side is formed by an opposite ray.*The sum of a linear pair is *

Two angles whose sum is . Two angles whose sum is

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Try Some

Examples

Determine if the following angles are vertical, complementary, or supplementary.

ANGLE RELATIONSHIPS EXAMPLES

Show Answer

complementary

Show Answer

vertical

Show Answer

supplementary

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More Example

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Refer to the figure to answer the following questions.

ANGLE RELATIONSHIP EXAMPLES

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More Example

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Show Answer

and and

Show Answer

𝑚∠2=43 °

Show Answer

𝑚∠3=143 °

Use the diagram to answer the questions.

ANGLE RELATIONSHIP EXAMPLES

Show Answer ∠𝐶𝐵𝐷=31 °

Show Answer

or

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More Example

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ANGLE RELATIONSHIP EXAMPLES

Use the diagram to answer the questions.

Show Answer ∠𝐶𝐵𝐷=61 °

Show Answer 𝑥=

803𝑜𝑟 26.66

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More Example

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Use the diagram shown to answer the question.

ANGLE RELATIONSHIPS

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Show Answer

. If then so is not perpendicular to

TRIANGLES

The Triangle Sum Theorem:

For any triangle, the sum of all interior angles is .

.

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TRIANGLES

The Exterior Angle Theorem:For any triangle, an exterior angle is equal to the sum of the non-adjacent interior angles.

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CLASSIFYING TRIANGLES

By Sides:

Equilateral: 3 congruent sides

Isosceles: 2 congruent sides

Scalene: No congruent sides

By Angles:

Acute triangle: contains 3 acute angles

Equiangular triangle: contains 3 congruent angles (must be .

Right triangle: contains one right angle

Obtuse triangle: contains one obtuse angle

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Try Some

Examples

Use the diagram to answer the questions.

TRIANGLE EXAMPLES

Show Answer 𝑚∠2=36 °

Show Answer

Show Answer Return

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More Example

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Use the diagram shown to answer the questions.

TRIANGLE EXAMPLES

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Show Answer

ISOSCELES AND EQUILATERAL TRIANGLES

Equilateral:

3 congruent sides3 congruent angles ()

Isosceles:

2 congruent sides (legs) (non-congruent side is the base)2 congruent angles (base angles) (non-congruent angle is the vertex)

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Try Some

Examples

Find the value of x in each diagram.

EXAMPLES

Show Answer

𝑥=26

Show Answer

𝑥=61

Show Answer

𝑥=110

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