1 / 3

EXAMPLE 4

AB DE. BC EF. m B > m E. Proof : Assume temporarily that m B > m E . Then, it follows that either m B = m E or m B < m E . EXAMPLE 4. Prove the Converse of the Hinge Theorem. Write an indirect proof of Theorem 5.14 . GIVEN :. AC > DF. PROVE:.

elin
Download Presentation

EXAMPLE 4

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. AB DE BC EF m B > m E Proof : Assume temporarily that m B > m E. Then, it follows that either mB = m E orm B < m E. EXAMPLE 4 Prove the Converse of the Hinge Theorem Write an indirect proof of Theorem 5.14. GIVEN : AC > DF PROVE:

  2. If m B = m E, then B E. So, ABC DEF by the SAS Congruence Postulate and AC =DF. If m B <m E, then AC < DFby the Hinge Theorem. Both conclusions contradict the given statement that AC > DF. So, the temporary assumption that m B > m Ecannot be true. This proves that m B > m E. EXAMPLE 4 Prove the Converse of the Hinge Theorem Case 1 Case 2

  3. The third side of the first is less than or equal to the third side of the second; Case 1: Third side of the first equals the third side of the second. is less than the third side of the second. Case 2: Third side of the first for Example 4 GUIDED PRACTICE 5. Write a temporary assumption you could make to prove the Hinge Theorem indirectly. What two cases does that assumption lead to? SOLUTION

More Related