1. Congruency and Triangles Featuring Right Triangles Section 4.6

2. Lesson Objectives  Learn the properties of congruent right triangles.  Learn the properties of perpendicular bisectors.

3. Review : Right Triangles  Recall that right triangles are composed of a hypotenuse which is opposite the right angle and two legs. If the two legs are not equal in length they are referred to as the short leg and long leg of the triangle.

4. Theorem 4-5: The Perpendicular Bisector Theorem: If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base.

5. Theorem 4-6: The Hypotenuse-Leg (HL) Theorem Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. Then Δ ABC ≅ Δ DEF

6. Theorem 4-6: The Hypotenuse-Leg (HL) Theorem

7. Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

8. Theorem 4-6: The Hypotenuse-Leg (HL) Theorem

10. Practice What additional information do you need to prove the triangles are congruent by HL? Δ ABC ≅ Δ XYZ Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

11. Practice What additional information do you need to prove the triangles are congruent by HL? Δ ABC ≅ Δ DCB Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

12. Practice What additional information do you need to prove the triangles are congruent by HL? ΔSTR ≅ ΔPQN Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

13. Practice For what values of x and y are the triangles congruent by HL? Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

14. Practice For what values of x and y are the triangles congruent by HL? Conditions:  There are two right triangles  The triangles have congruent hypotenuses  There is one pair of congruent legs

15. Proofs using the HL Theorem

16. Exit Slip Self-assessment: at the bottom of your answer sheet write down how well you understand this concept from 1 : 4 1 (don’t understand) 2 (kind of understand) 3 (understand but may need a little help) 4 (understand and can explain it to others)