1. Warm Up

2. Indirect Proof Chapter 5.1 Objective- Write Indirect Proofs

3. Indirect Proofs are…? An indirect Proof is used in a problem where a direct proof would be difficult to apply Used to contradict the given fact or a theorem or definition

4. Given: DB AC M is midpoint of AC Prove: AD ≠ CD D CMB A T ~

5. In order for AD and CD to be congruent, Δ ADC must be isosceles. But then the foot (point B) of the altitude from the vertex D and the midpoint M of the side opposite the vertex D would have to coincide. Therefore, AD ≠ DC unless point B = point M. ~

6. Rules: List the possibilities for the conclusion Assume negation of the desired conclusion is correct Write a chain of reasons until you reach an impossibility Contradiction of information, theorem definition or know fact State the remaining possibility as the desired conclusion

7. Given:<H ≠ <K Prove: JH ≠ JK »Either JH is congruent to JK or it’s not »Assume JH is congruent to JK, then ΔHJK is isosceles because of congruent segments »Then <H is congruent to <K »Since <H isn’t congruent to <K, then JH isn’t congruent to JK ~ ~ J H K

8. Given: MATH is a square In terms of a, find M and A T (2a, 0) H (0, 0) M A What is the area of MATH? What is the midpoint of MT? (2a.2a) (0,2a) What are the coordinates of A and M? A = 4a 2 (a,a)