1. 4.6 Congruence in Right Triangles I can prove triangles congruent by using Hypotenuse – Leg Theorem.
Do Now:
Identify the postulate or theorem that proves the triangles congruent.
SSS
ASA
SAS or SSS
Success Criteria:
Today’s Agenda
Prove triangles congruent by hypotenuse leg
Prove parts congruent and measure distance
Do Now
Check HW
Lesson
Assignment

2. HW #32 Answer pg 243 # 1-19 all

4. Conditions for HL Theorem:
There are two right triangles
The triangles have congruent hypotenuse
There is one pair of congruent legs

5. Example 4A: Applying HL Congruence
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.
According to the diagram, the triangles are right triangles that share one leg.
It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.

6. Example 4B: Applying HL Congruence
This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.

7. Check It Out! Example 4
Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know.
Yes; it is given that AC  DB. BC  CB by the Reflexive Property of Congruence. Since ABC and DCB are right angles, ABC and DCB are right triangles. ABC  DCB by HL.

8. Proof Practice: Don’t peek at answer, try it!!
4. Given: FAB  GED, ABC   EDC, AC  EC
Prove: ABC  EDC

9. Lesson Quiz: Part II Continued
5. AAS Steps 3,4
5. ABC  EDC
4. Given
4. ACB  EDC; AC  EC
3.  Supp. Thm.
3. BAC  DEC
2. Def. of supp. s
2. BAC is a supp. of FAB; DEC is a supp. of GED.
1. Given
1. FAB  GED
Reasons
Statements

10. Assignment #33 pg
P: # , 34 – 36 If you finish early please watch the video from your book and/or try the Geometry Quizzes on Dragonometry.net