12/16/09 Do Now Label the hypotenuse, legs, and acute angles of the following right triangles. A C B D E

Right Triangles 5-2 Objective: Prove triangles congruent using the LL, HA, LA, and HL theorems

5-2: Right Triangles The Leg-Leg Theorem (LL) If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

5-2: Right Triangles The Leg-Leg Theorem (LL) If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. A B C Y X Z

5-2: Right Triangles The Hypotenuse-Angle Theorem (HA) If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.

5-2: Right Triangles The Hypotenuse-Angle Theorem (HA) If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent. Q R S U T V

5-2: Right Triangles The Leg-Angle Theorem (LA) If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

5-2: Right Triangles The Leg-Angle Theorem (LA) If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent. T W O A P C

5-2: Right Triangles The Hypotenuse-Leg Theorem (HL) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

5-2: Right Triangles The Hypotenuse-Leg Theorem (HL) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. B I G U P N

5-2: Right Triangles Example 1 – State the theorem or method that would be used to prove the following right triangles congruent. Then make a congruence statement about the triangles. B A DE R

5-2: Right Triangles Example 2 – State the theorem or method that would be used to prove the following right triangles congruent. Then make a congruence statement about the triangles. CA O T

5-2: Right Triangles Homework Pg #4-12 and #14-18

5-2: Right Triangles