Presentation on theme: "EXAMPLE 4 Prove the Converse of the Hinge Theorem"— Presentation transcript:
1EXAMPLE 4Prove the Converse of the Hinge TheoremWrite an indirect proof of Theorem 5.14.GIVEN :AB DEBC EFAC > DFPROVE:m B > m EProof : Assume temporarily that m B > m E. Then, it follows that eitherm B = m E or m B < m E.
2EXAMPLE 4Prove the Converse of the Hinge TheoremCase 1If m B = m E, then B E So, ABC DEF by the SAS Congruence Postulate and AC =DF.Case 2If 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.
3GUIDED PRACTICEfor Example 45.Write a temporary assumption you could make to prove the Hinge Theorem indirectly. What two cases does that assumption lead to?SOLUTIONThe 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