Download presentation

Presentation is loading. Please wait.

Published byMackenzie Parsons Modified over 4 years ago

1
**When 2 lines intersect we see 4 individual angles formed.**

Chap 2 Sec 4 Vertical Angles and Linear Pairs When 2 lines intersect we see 4 individual angles formed. 1 2 3 4 We usually talk about these angles 2 at a time. The term we use depends on which 2 angles we are talking about. If the 2 angles are across from each other (not adjacent), then they are called vertical angles. If the 2 angles are beside each other (adjacent), then they are called a linear pair. 1

2
**Vertical angles are congruent.**

Chap 2 Sec 4 Vertical Angles and Linear Pairs 1 2 3 4 Recognizing these angle pairs is important because they have special relationships. Vertical angles are congruent. Linear pairs are supplementary (180°). 2

3
**Determine whether the labeled angles are vertical angles, **

Example 1 Identify Vertical Angles and Linear Pairs Determine whether the labeled angles are vertical angles, a linear pair, or neither. b. a. c. SOLUTION a. 1 and 2 are a linear pair because they are adjacent and their noncommon sides are on the same line. b. 3 and 4 are neither vertical angles nor a linear pair. c. 5 and 6 are vertical angles because they are not adjacent and their sides are formed by two intersecting lines. 3

4
**Find the measure of RSU.**

Example 2 Use the Linear Pair Postulate Find the measure of RSU. SOLUTION RSU and UST are a linear pair. By the Linear Pair Postulate, they are supplementary. To find mRSU, subtract mUST from 180°. mRSU = 180° – mUST = 180° – 62° = 118° 4

5
**Find the measure of CED.**

Example 3 Use the Vertical Angles Theorem Find the measure of CED. SOLUTION AEB and CED are vertical angles. By the Vertical Angles Theorem, CED AEB, so mCED = mAEB = 50°. 5

6
**Example 4 Find m1, m2, and m3. SOLUTION m2 = 35°**

Find Angle Measures Find m1, m2, and m3. SOLUTION m2 = 35° Vertical Angles Theorem m1 = 180° – 35° = 145° Linear Pair Postulate m3 = m1 = 145° Vertical Angles Theorem 6

7
**Checkpoint Find m1, m2, and m3. 1.**

Find Angle Measures Find m1, m2, and m3. 1. ANSWER m1 = 152°; m2 = 28°; m3 = 152° 2. ANSWER m1 = 56°; m2 = 124°; m3 = 56° 3. ANSWER m1 = 113°; m2 = 67°; m3 = 113°

8
**Example 5 Find the value of y. SOLUTION**

Use Algebra with Vertical Angles Find the value of y. SOLUTION Because the two expressions are measures of vertical angles, you can write the following equation. (4y – 42)° = 2y° Vertical Angles Theorem 4y – 42 – 4y = 2y – 4y Subtract 4y from each side. –42 = –2y Simplify. –2 –42 –2y = Divide each side by –2. 21 = y Simplify. 8

9
**Find the value of the variable.**

Checkpoint Use Algebra with Angle Measures Find the value of the variable. 4. ANSWER 43 5. ANSWER 16 6. ANSWER 5

Similar presentations

OK

Angles Acute angle (def)- angle measure less than 90° Right angle (def)- angle measure= 90° Obtuse angle (def)- angle measure greater than 90° Straight.

Angles Acute angle (def)- angle measure less than 90° Right angle (def)- angle measure= 90° Obtuse angle (def)- angle measure greater than 90° Straight.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google