Proving Congruence SSS, SAS Postulate 4.1 Side-Side-Side Congruence If the sides of one triangle are congruent to the sides of a second triangle, then.

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4-2 Triangle Congruence by SSS and SAS

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Presentation transcript:

Proving Congruence SSS, SAS Postulate 4.1 Side-Side-Side Congruence If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Postulate 4.2 Side-Angle-Side Congruence If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that  FEG  HIG and G is the midpoint of both

Given: G is the midpoint of both Prove: 1. Given1. Proof: ReasonsStatements 3. SSS3.  FEG  HIG  FEG  HIG 2. Midpoint Theorem2.

3. SSS 1. Given 2. Reflexive Proof: ReasonsStatements  ABC  GBC Write a two-column proof to prove that  ABC  GBC if

Use the Distance Formula to show that the corresponding sides are congruent. COORDINATE GEOMETRY Determine whether  WDV  MLP for D (–5, –1), V (–1, –2), W (–7, –4), L (1, –5), P (2, –1), and M (4, –7). Explain.

Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore,  WDV  MLP by SSS.

Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore,  ABC  DEF by SSS. Determine whether  ABC  DEF for A (5, 5), B (0, 3), C (–4, 1), D (6, –3), E (1, –1), and F (5, 1). Explain.

Write a flow proof. Given: Prove:  QRT  STR

Answer:

Write a flow proof. Given:. Prove:  ABC  ADC

Proof:

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. Answer: SAS Two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle. The triangles are congruent by SAS.

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. Answer: SSS Each pair of corresponding sides are congruent. Two are given and the third is congruent by Reflexive Property. So the triangles are congruent by SSS.

Answer: SAS Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. a.

Answer: not possible b.