shannonblair
Uploaded by
19 SLIDES
209 VUES
190LIKES

Congruence Theorems for Right and Vertical Angles

DESCRIPTION

Learn and apply the Right Angle Congruence Theorem and the Vertical Angles Congruence Theorem to prove the congruence of angles in geometric problems.

1 / 19

Télécharger la présentation

Congruence Theorems for Right and Vertical Angles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. REASONS STATEMENT EXAMPLE 1 Use right angle congruence Theorem: Right Angle Congruence Theorem All right angles are congruent Given: <1 and <2 are right angles Prove: <1 is congruent to <2

  2. ABBC, DCBC GIVEN: BC PROVE: REASONS STATEMENT 1. 1. ABBC, DCBC Given 2. 2. Definition of perpendicular lines Band Care right angles. 3. BC 3. Right Angles Congruence Theorem EXAMPLE 1 Use right angle congruence Write a proof.

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

  4. REASONS STATEMENT 1. 1. 1 and 2 are supplements. Given 3 and 2 are supplements. 2. 2. m1+m2= 180° Definition of supplementary angles m3+m2= 180° 3. m3+m2 3. m1+m2= Transitive Property of Equality 4. m1=m3 4. Subtraction Property of Equality 5. • 3 5. Definition of congruent angles EXAMPLE 2 Prove a case of Congruent Supplements Theorem

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

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

  7. Statements (Reasons) 1.1 and 3 are complements; 3 and 5 are complements. (Given) 2.∠ 1 5 (Congruent Complements Theorem.) for Examples 1 and 2 GUIDED PRACTICE

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

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

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

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

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

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

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

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

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

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

More Related