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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.
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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
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Given: G is the midpoint of both Prove: 1. Given1. Proof: ReasonsStatements 3. SSS3. FEG HIG FEG HIG 2. Midpoint Theorem2.
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3. SSS 1. Given 2. Reflexive Proof: ReasonsStatements 1. 2. 3. ABC GBC Write a two-column proof to prove that ABC GBC if
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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.
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Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS.
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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.
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Write a flow proof. Given: Prove: QRT STR
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Answer:
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Write a flow proof. Given:. Prove: ABC ADC
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Proof:
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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.
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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.
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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.
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Answer: not possible b.
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