b. ΔTUW  ΔQOS by AAS ΔTUW  ΔQOS by SAS ∠T  ∠Q TU  QO What information is missing to say that: b. ΔTUW  ΔQOS by AAS ΔTUW  ΔQOS by SAS ∠T  ∠Q TU  QO

4.7 Cont. HL Objectives: Apply HL to construct triangles and to solve problems. Prove triangles congruent by using HL.

The bad word one… SSA or ASS….. We cannot use this to prove two triangles are congruent. It’s a bad word, it’s bad news, and it doesn’t work… so NEVER use it!

I think of this one as rASS

HL-RT In a HL proof you need 3 things The hypotenuse The leg Tell us that the triangles have a right angle, thus making them right triangles. Therefore, HL is only used in RIGHT Triangles!!!! HL-RT

K L M N Example 1A: 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. K 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. L M N

Example 1B: 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.

Check It Out! Example 2 Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know. Yes, so lets prove it!

USE: HL-RT CB≅BC H L RT 1. Given 2. Reflexive Property 3. Given ✔ ✔ ✔ USE: HL-RT Statements Reasons 1. Given H CB≅BC 2. Reflexive Property L 3. Given 4. A right triangle has 1 right angle RT 5. HL

Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

Lesson Quiz: Part II 4. Given: FAB  GED, ACB   ECD, AC  EC Prove: ABC  EDC

Lesson Quiz: Part II Continued 5. ASA 5. ABC  EDC 4. Given 4. ACB  DCE; 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