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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