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2.4 – Vertical Angles

2.4 – Vertical Angles. Homework #5 Objectives #9, #10. Activity 2.4 – Angles and Intersecting Lines. On a piece of paper, draw line l using the straightedge of your protractor. Label two points A and B towards the end of the line. Activity 2.4 – Angles and Intersecting Lines.

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2.4 – Vertical Angles

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  1. 2.4 – Vertical Angles Homework #5 Objectives #9, #10

  2. Activity 2.4 – Angles and Intersecting Lines • On a piece of paper, draw line l using the straightedge of your protractor. Label two points A and B towards the end of the line.

  3. Activity 2.4 – Angles and Intersecting Lines • Draw line m so that it intersects line l. Label the point of intersection E. Label the points C and D towards the ends of line m.

  4. Activity 2.4 – Angles and Intersecting Lines • Use the protractor to measure (and record) the four angles formed by the intersecting lines.

  5. Activity 2.4 – Angles and Intersecting Lines • What do you notice about the nonadjacent angles you measured? • Find the sum of the measures of any two adjacent angles you measured. What do you notice?

  6. Defining Vertical Angles • Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines.

  7. Defining Linear Pair • Two adjacent angles are a linear pair if their non-common sides are on the same line.

  8. Example 1 Determine whether the labeled angles are vertical angles, a linear pair,or neither. SOLUTION Identify Vertical Angles and Linear Pairs b. c. a. 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6are vertical angles because they are not adjacent and their sides are formed by two intersecting lines.

  9. Linear Pair Postulate

  10. Example 2 Find the measure of RSU. SOLUTION RSU andUST are a linear pair. By the Linear Pair Postulate, they are supplementary. To findmRSU,subtract mUST from180°. mRSU =180°– mUST = 180°–62° = 118° Use the Linear Pair Postulate

  11. Vertical Angle Theorem

  12. Example 3 Find the measure of CED. SOLUTION AEBandCED are vertical angles. By the Vertical Angles Theorem,CED AEB,so mCED = mAEB = 50°. Use the Vertical Angles Theorem

  13. Example 4 Findm1, m2,andm3. SOLUTION Find Angle Measures m2 = 35° Vertical Angles Theorem m1 = 180° – 35° = 145° LinearPairPostulate m3 = m1= 145° Vertical Angles Theorem

  14. Checkpoint Findm1, m2,andm3. Find Angle Measures 1. m1 = 152°; m2 = 28°;m3 = 152° ANSWER 2. m1 = 56°; m2 = 124°;m3 = 56° ANSWER 3. m1 = 113°; m2 = 67°;m3 = 113° ANSWER

  15. Example 5 SOLUTION Because the two expressions are measures of vertical angles, you can write the following equation. –2y = Divide each side by –2. –2 Use Algebra with Vertical Angles Find the value of y. (4y– 42)° = 2y° Vertical Angles Theorem 4y– 42 – 4y= 2y – 4y Subtract 4y from each side. –42 = –2y Simplify. –42 21 = y –2 Simplify.

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

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