Download presentation

Presentation is loading. Please wait.

Published byMichael Kneebone Modified over 3 years ago

1
EXAMPLE 4 Prove the Converse of the Hinge Theorem Write an indirect proof of Theorem 5.14. GIVEN : AB DE BC EF AC > DF PROVE: 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.

2
EXAMPLE 4 Prove the Converse of the Hinge Theorem Case 1 If m B = m E, then B E So, ABC DEF by the SAS Congruence Postulate and AC =DF. Case 2 If m B < m E, then AC < DF by the Hinge Theorem. Both conclusions contradict the given statement that AC > DF. So, the temporary assumption that m B > m E cannot be true. This proves that m B > m E.

3
GUIDED PRACTICE for Example 4 5. Write a temporary assumption you could make to prove the Hinge Theorem indirectly. What two cases does that assumption lead to? SOLUTION 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

Similar presentations

Presentation is loading. Please wait....

OK

Inequalities in Two Triangles

Inequalities in Two Triangles

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Training ppt on email etiquettes Ppt on 1857 the first war of independence Ppt on c language fundamentals Ppt on leadership theories Jit ppt on manufacturing definition Ppt on business etiquettes ppt Ppt on tata trucks new Ppt on standing order definition Ppt on earth day Ppt on how industries are polluting our water resources