1. LESSON TWELVE: CONGRUENCE THE RIGHT WAY

2. CONGRUENCE As we have discovered, there are many congruence theorems for all types of triangles. As we will find out in the coming days, some types or triangles have unique properties.

3. RIGHT TRIANGLE CONGRUENCE Right Triangles are one type that have special properties. We will discuss four of them. As we introduced these, notice the similarities between our original congruence postulates.

4. RIGHT TRIANGLE CONGRUENCE The first theorem for right angles we’ll learn is the Leg-Leg Congruence Theorem. This says that if the legs of one right triangle, are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

5. RIGHT TRIANGLE CONGRUENCE

6. The next theorem for right angles is the Hypotenuse-Angle Congruence Theorem. This says if the hypotenuse and acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle then the two triangles are congruent.

7. RIGHT TRIANGLE CONGRUENCE

8. The third theorem in our lineup is the Leg- Angle Congruence Theorem. This says that 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.

9. RIGHT TRIANGLE CONGRUENCE

10. Finally, the Hypotenuse-Leg Theorem. This says that 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.

11. RIGHT TRIANGLE CONGRUENCE

12. We can use these theorems in proofs the same way as we can use any of the other properties, postulates or theorems we have learned.

13. RIGHT TRIANGLE CONGRUENCE A M C B

14. STATEMENTS JUSTIFICATION 1.Given 2.Definition of Bisector 3.Definition of Perpendicular Lines. 4.Definition of Right Triangles 5.Reflexive Property 6.LL Congruence A M C B

15. RIGHT TRIANGLE CONGRUENCE The only difference between these proofs and the ones we have already done is that we need to occasionally prove that we are, in fact, dealing with a right triangle. Sometimes it is given, sometimes not. Without that, we cannot use any of these theorems.