Lesson 1-5

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# Lesson 1-5 - PowerPoint PPT Presentation

Lesson 1-5. Angle Relationships. Lesson Outline. Five-Minute Check Then &amp; Now and Objectives Vocabulary Key Concept Examples Lesson Checkpoints Summary and Homework. Then and Now. You measured and classified angles. Identify and use special pairs of angles

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### Lesson 1-5

Angle Relationships

Lesson Outline
• Five-Minute Check
• Then & Now and Objectives
• Vocabulary
• Key Concept
• Examples
• Lesson Checkpoints
• Summary and Homework
Then and Now

You measured and classified angles.

• Identify and use special pairs of angles
• Identify perpendicular lines
Objectives
• Identify and use special pairs of angles
• Identify perpendicular lines
Vocabulary
• Adjacent angles – two coplanar angles that have a common vertex, a common side, but no common interior points
• Linear pair – a pair of adjacent angles whose noncommon sides are opposite rays (always supplementary)
• Vertical angles – two non adjacent angles formed by two intersecting lines

Vertical angles are congruent (measures are equal)!!

• Complementary Angles – two angles whose measures sum to 90°
• Supplementary Angles – two angles whose measures sum to 180°
• Perpendicular – two lines or rays are perpendicular if the angle (s) formed measure 90°
Key Concept

Looks like:

• Y (on its side)
• X
Example 1A

A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.

A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.

Sample Answers: PIQ and QIS, PIT and TIS, QIU and UIT

Example 1B

B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.

Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU

Key Concept
• m = m
Example 2

ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

Let the measure of one angle be x.

Solve

Given

6x – 6 = 180 Simplify.

6x = 186 Add 6 to each side.

x = 31 Divide each side by 6.

Example 2 cont

ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

Use the value of x to find each angle measure.

mA = x mB = 5x – 6

= 31 = 5(31) – 6 or 149

CheckAdd the angle measures to verify that the angles are supplementary.

mA + mB = 180

31 + 149 = 180

180 = 180 

Answer:mA = 31, mB = 149

Key Concept
• perpendicular means right angle

ALGEBRA Find x and y so thatKO and HM are perpendicular.

Example 3

If KO HM, then mKJH = 90. To find x, use KJI and IJH

Example 3 cont

mKJH = mKJI + mIJH Sum of parts = whole

90 = (3x + 6) + 9x Substitution

90 = 12x + 6 Combine like terms.

84 = 12x Subtract 6 from each side.

7 = x Divide each side by 12.

To find y, use mMJO.

mMJO = 3y + 6 Given

90 = 3y + 6 Substitution

84 = 3y Subtract 6 from each side.

28 = y Divide each side by 3.

Answer: x = 7 and y = 28

Key Concept
• Be careful what you assume!
• 89° and 91° may be hard to tell apart from 90°
Example 4A

Answer: Yes; VY and TX are perpendicular

A. Determine whether the following statement can be justified from the figure below. Explain.

mVYT = 90

The diagram is marked to show that VY  TX. From the definition of perpendicular, perpendicular lines intersect to form congruent adjacent angles.

Example 4B

B. Determine whether the following statement can be justified from the figure below. Explain.

TYW andTYU are supplementary.

Answer: Yes, they form a linear pair of angles.

Example 4C

C. Determine whether the following statement can be justified from the figure below. Explain.

Answer: No, they do not share a common side.

Summary & Homework
• Summary:
• There are many special pairs of angles such as adjacent angles, vertical angles, complementary angles, supplementary angles, and linear pairs.
• Homework:
• pg 50-3: 8-15, 19-22