Copyright © by Holt, Rinehart and Winston
Reteach
Triangle Congruence: ASA, AAS, and HL
Determine whether you can use ASA to prove the triangles congruent. Explain.
[pic] [pic]
1. (KLM and (NPQ 2. (EFG and (XYZ
[pic] [pic]
3. (KLM and (PNM, given that M is the 4. (STW and (UTV
midpoint of [pic]
Reteach
Triangle Congruence: ASA, AAS, and HL continued
\
Special theorems can be used to prove right triangles congruent.
5. Describe the corresponding parts and the justifications
for using them to prove the triangles congruent by AAS.
Given: [pic] is the angle bisector of ∠ADC.
Prove: (ABD > (CBD
Determine whether you can use the HL Congruence Theorem to prove the triangles congruent. If yes, explain. If not, tell what else you need to know.
[pic] [pic]
6. (UVW > (WXU 7. (TSR > (PQR
Reteach
1. Yes; (K ( (N, [pic] and (L ( (P as given.
2. No; you need to know that [pic]
3. No; you need to know that (NMP ( (LMK.
4. Yes; (W ( (V, [pic] as given. (STW ( (UTV by the Vert. [pic] Thm.
5. (A ( (C (Given), (ADB ( (CDB (Def. of ( bisector), [pic] (Reflex. Prop. of ()
6. Yes; [pic] (Given) and [pic] (Reflex. Prop. of ()
7. No; you need to know that [pic]
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|Angle-Side-Angle (ASA) Congruence Postulate |
|If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the |
|triangles are congruent. |
[pic] is the included side of /D and /F.
[pic] is the included side of /A and /C.
|Angle-Angle-Side (AAS) Congruence Theorem |
|If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle,|
|then the triangles are congruent. |
|[pic] |
[pic] is a nonincluded side of /F and /G.
[pic] is a nonincluded side of /J and /K.
|Hypotenuse-Leg (HL) Congruence Theorem |
|If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles |
|are congruent. |
|[pic] |
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