WarmUp 1 Exercises EXAMPLE Use right angle congruence

Warm-Up 1 Exercises EXAMPLE Use right angle congruence Write a proof. AB GIVEN: BC , DC B PROVE: C REASONS STATEMENT 1. AB 2. 3. BC , DC B and angles. B BC C are right C BC 1. Given 2. Definition of perpendicular lines 3. Right Angles Congruence Theorem

Warm-Up 2 Exercises EXAMPLE Prove a case of Congruent Supplements Theorem Prove that two angles supplementary to the same angle are congruent. GIVEN: 1 and 2 are supplements. 3 and 2 are supplements. PROVE: 1 3

Warm-Up 2 Exercises EXAMPLE Prove a case of Congruent Supplements Theorem REASONS STATEMENT 1. 1 and 3 and 2 are supplements. 1. Given 2 are supplements. 2. m 1+ m m 3+ m 3. m 1+m 4. m 1=m 5. 1 2. Definition of 2 = 180° 2= m 3 3 supplementary angles 3+m 2 3. Transitive Property of Equality 4. Subtraction Property of Equality 5. Definition of congruent angles

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 1. How many steps do you save in the proof in Example 1 by using the Right Angles Congruence Theorem? ANSWER 2 Steps 2. Draw a diagram and write GIVEN and PROVE statements for a proof of each case of the Congruent Complements Theorem.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 ANSWER Write a proof. Given: 1 and 3 and Prove: ∠ 1 3 are complements; 5 are complements. 5

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Statements (Reasons) 1. 1 and 3 are complements; 5 are complements. (Given) 2. ∠ 1 5 (Congruent Complements Theorem. )

Warm-Up 3 Exercises EXAMPLE Prove the Vertical Angles Congruence Theorem Prove vertical angles are congruent. GIVEN: 5 and PROVE: ∠ 5 ∠ 7 are vertical angles. 7

Warm-Up 3 Exercises EXAMPLE Prove the Vertical Angles Congruence Theorem STATEMENT REASONS 1. 5 and 7 are vertical angles. 1. Given 2. 5 and 6 and 7 are a linear pair. 3. 5 and 6 and 7 are supplementary. 3. Linear Pair Postulate 7 are supplementary. 4. ∠ 5 ∠ 7 2. Definition of linear pair, as shown in the diagram 4. Congruent Supplements Theorem

Warm-Up Exercises GUIDED PRACTICE for Example 3 In Exercises 3– 5, use the diagram. 3. If m 1 = 112°, find m ANSWER m 2 = 68° m 3 = 112° m 4 = 68° 2, m 3, and m 4.

Warm-Up Exercises GUIDED PRACTICE 4. If m for Example 3 2 = 67°, find m 1, m 3, and m 4. 1, m 2, and m 3. ANSWER m 1 = 113° 5. m 3 = 113° m 4 = 67° If m 4 = 71°, find m ANSWER m 1 = 109° m 2 = 71° m 3 = 109°

Warm-Up Exercises GUIDED PRACTICE 6. for Example 3 Which previously proven theorem is used in Example 3 as a reason? ANSWER Congruent Supplements Theorem

Warm-Up 4 Exercises EXAMPLE Standardized Test Practice SOLUTION Because TPQ and QPR form a linear pair, the sum of their measures is 180. ANSWER The correct answer is B.

Warm-Up Exercises GUIDED PRACTICE for Example 4 Use the diagram in Example 4. 7. Solve for x. ANSWER x = 49

Warm-Up Exercises GUIDED PRACTICE for Example 4 Use the diagram in Example 4. 8. Find m TPS. ANSWER m TPS = 148°

Daily Homework Quiz Warm-Up Exercises 1. Give the reason for each step 5 GIVEN : 1 PROVE : 1 is supplementary to Statements (Reasons) 1. 1 5 (Given) ANSWER 2. m 1=m ANSWER 3. 4 and ANSWER 5 (Def. of ) 5 are a linear pair. (Def. of linear pair ) 4

Daily Homework Quiz Warm-Up Exercises 4. 4 and (Linear Pair Post. ) ANSWER 5. m 4+m ANSWER 7. 5 = 180 (Def. of supplementary ) ANSWER 6. m 5 are supplementary. 1 = 180 (Substitution Prop. of Eq. ) 1 is supplementary to ANSWER 4. (Def. of supplementary )