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Transcript
Angle Proofs Name: _________________ Period: ______ Teacher: _______________ Table of Contents Day 1: SWBAT Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems Pages 2-8 HW: pages 9-11 Day 2: SWBAT Write two-column angle proofs involving supplementary and complementary angles Pages 12-14 HW: pages 15-16 Day 3: SWBAT Write two-column angle proofs involving supplementary and complementary angles Pages 17-19 HW: pages 20-23 Day 4: REVIEW Day 5: Exam Angle Theorems If two angles are right angles, then they are congruent. If two angles are vertical angles, then they are congruent. If two angles are complements of the same angle, then they are congruent. If two angles are congruent, then their complements are congruent. If two angles are supplements of the same angle, then they are congruent. If two angles are congruent, then their supplements are congruent. If two angles form a linear pair, then they are supplementary If two angles are vertical angles, then they are congruent. Additional Theorem: Radii of a circle are congruent. Radii of congruent circles are congruent. 1 Name________________________ Date_________________________ Geometry Day1: Proofs with Angles SWBAT: Recognize complementary and supplementary angles and prove angles congruent by means of four new theorems Warm - Up 2 Example 1: You Try It! Given: Prove: CONV: If the sum of two s is a straight (180), then they are supplementary. 3 Example 2: 2. 4 3. 4. When to use these theorems??? When 2 pairs of angles are complementary or supplementary to the SAME angle or CONGRUENT angles. Strategy: In statements, look for double use of the word “complementary” or “supplementary” AND for a congruence statement. Circle the angles indicated by the congruence statement, and the uncircled angles will be congruent! You don’t even need to look at a diagram! 5 Practice Proof Writing 1. 2. Given: 1 4 Prove: 2 3 6 O 3. Given: OA and MP intersect at T Prove: 1 2 M 1 T 2 P A Summary 7 Exit Ticket K R P Given: KMR POR Prove: ROM RMO Statement O M Reason 8 Day 1 - Homework 1. Given: 1 2 Prove: 3 4 2. Given: 2 4 Prove: 1 3 1 2 3 4 9 3. Given: Prove: O is complementary to 2 J is complementary to 1 O J 4. 10 5. T 6. Given: TR RQ TS SQ 3 4 Prove: 1 2 R 2 4 1 3 S Q 11 Name________________________ Date_________________________ Geometry Day2: More Practice Writing Proofs with Angles SWBAT: Write two-column angle proofs involving supplementary and complementary angles. Warm - Up 12 1. Given: F is complementary to FGJ H is complementary to HGJ GJ Bisects FGH Prove: F H 2. Given: Prove: FKJ is a right angle. HJK is a right angle GKJ GJK FKG HJG 13 3) 4) 14 Day 2 - Homework 5) 15 7) 8) 16 Name________________________ Date_________________________ Geometry Day3: More Practice Writing Proofs with Angles SWBAT: Write two-column angle proofs involving supplementary and complementary angles. Warm -Up 17 1. 2. 18 3. 4. 19 Day 3 - Homework 5. 6. 20 7. 8. Given: Prove: 21 9. 22 10. 23