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4.4 – Prove Triangles Congruent by SAS

4.4 – Prove Triangles Congruent by SAS. Geometry Ms. Rinaldi. Included Angles. The included angle is the angle between two sides. Side-Angle-Side (SAS) Congruence Postulate. B.

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4.4 – Prove Triangles Congruent by SAS

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  1. 4.4 – Prove Triangles Congruent by SAS Geometry Ms. Rinaldi

  2. Included Angles The included angle is the angle between two sides.

  3. Side-Angle-Side (SAS) Congruence Postulate B If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If Side Angle Side Then C A S T R

  4. EXAMPLE 1 Use SAS Decide whether the congruence statement is true. Explain your reasoning. SOLUTION (S) (A) (S) So, by SAS,

  5. EXAMPLE 2 Use SAS Decide whether the congruence statement is true. Explain your reasoning. SOLUTION Although there are two pairs of congruent sides, the congruent angles are not included (between) the congruent sides. Therefore SAS does not apply and the triangles are not congruent.

  6. EXAMPLE 3 Use SAS Decide whether the congruence statement is true. Explain your reasoning. Hint: This is possible! Do not forget the side they both share!

  7. EXAMPLE 4 Use SAS Decide whether the congruence statement is true. Explain your reasoning. Hint: This is possible! You have the sides, you only need a pair of congruent angles in between…

  8. EXAMPLE 5 Use SAS Decide whether the congruence statement is true. Explain your reasoning. Hint: This is possible! Look for alternate interior angles as well as a side that both triangles share.

  9. Because they are vertical angles, PMQRMS. All points on a circle are the same distance from the center, so MP, MQ, MR, and MSare all equal. ANSWER MRSand MPQ are congruent by the SAS Congruence Postulate. EXAMPLE 6 Use SAS and properties of shapes In the diagram, QSand RPpass through the center Mof the circle. What can you conclude about MRSand MPQ? SOLUTION

  10. EXAMPLE 7 Use SSS or SAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the SSS Congruence Postulate. C A F D SOLUTION To use SSS, you need to know that

  11. EXAMPLE 8 Use SSS or SAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the SAS Congruence Postulate. C A F D SOLUTION To use SAS, you need to know that

  12. EXAMPLE 9 Use SSS or SAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the SAS Congruence Postulate. C A F D

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