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Proving Congruence SSS, SAS

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

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Proving Congruence SSS, SAS

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  1. 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.

  2. 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 Example 4-1a

  3. Given:G is the midpoint of both FEG HIG Proof: Statements Reasons 1. 1. Given 2. 2. Midpoint Theorem 3. FEG HIG 3. SSS Example 4-1b Prove:

  4. Write a two-column proof to prove that ABC GBC if 3. ABC GBC Proof: Statements Reasons 1. 1. Given 2. 2. Reflexive 3. SSS Example 4-1b

  5. COORDINATE GEOMETRYDetermine whether WDV MLPfor D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain. Example 4-2a Use the Distance Formula to show that the corresponding sides are congruent.

  6. Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS. Example 4-2b

  7. Determine whether ABC DEFfor A(5, 5), B(0, 3),C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain. Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, ABC DEF by SSS. Example 4-2c

  8. Write a flow proof. Given: Prove:QRT STR Example 4-3a

  9. Example 4-3b Answer:

  10. Write a flow proof. Given: . Prove:ABC ADC Example 4-3c

  11. Proof: Example 4-3d

  12. Example 4-4a 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. 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. Answer: SAS

  13. Example 4-4b 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. 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: SSS

  14. 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. Example 4-4c Answer: SAS

  15. b. Example 4-4d Answer: not possible

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