1. Check It Out! Example 1
Write an indirect proof that a triangle cannot have two right angles.
Step 1 Identify the conjecture to be proven.
Given: A triangle’s interior angles add up to 180°.
Prove: A triangle cannot have two right angles.
Step 2 Assume the opposite of the conclusion.
An angle has two right angles.

2. Check It Out! Example 1 Continued
Step 3 Use direct reasoning to lead to a contradiction.
m1 + m2 + m3 = 180°
90° + 90° + m3 = 180°
180° + m3 = 180°
m3 = 0°
However, by the Protractor Postulate, a triangle cannot have an angle with a measure of 0°.

3. Check It Out! Example 1 Continued
Step 4 Conclude that the original conjecture is true.
The assumption that a triangle can have two right angles is false.
Therefore a triangle cannot have two right angles.

4. 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.

5. 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.

6. Daily Homework Quiz 3.
Suppose you want to write an indirect proof of this statement: “In ABC, if m A > 90° then ABC is not a right triangle.” What temporary assumption should start your proof?
Assume ABC is a right triangle.
ANSWER