Week 13

5.6 – Indirect Proof and Inequalities in Two Triangles

Hinge Theorem  If two sides one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. Fancy talk for two sides same, one angle bigger than other, then side is bigger D A E B C F

Converse of Hinge Theorem  If two sides one triangle are congruent to two sides of another triangle, but the 3rd side of the first triangle is longer than the 3rd side of the second, then the included angle of the first triangle is larger than the included angle of the second. Fancy talk for two sides same, one sidee bigger than other, then angle is bigger D A E B C F

List the angles and sides in order U U 2 35o 1 14 45o 30o D D 70o C 70o 13 C K K ____ < ____ < ____ ____ < ____ student

Indirect Proof How to write an indirect proof 1. Assume temporarily that the conclusion is not true. 2. Reason logically until you reach a contradiction of the known fact. 3. Point out the temporary assumption is false, so the conclusion must be true.

Practice  Write the untrue conclusion

1 a 3 b

a 1 3 b