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Understanding Congruency Postulates in Geometry

This resource explores congruency postulates in geometric figures, focusing on the conditions that must be met for two shapes, particularly triangles, to be considered congruent. Key postulates such as Side-Side-Side (SSS) and Side-Angle-Side (SAS) are explained in detail, providing examples and proofs. The video includes problem-solving exercises to reinforce understanding, where students must determine congruency based on given information. This material is essential for mastering geometric congruency in classrooms and exams.

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Understanding Congruency Postulates in Geometry

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Presentation Transcript

  1. 4-2: Congruency Postulates

  2. What do we know about congruency so far? F B G C A E H D All corresponding sides and angles must be equal for the two shapes to be congruent!

  3. Side-Side-Side Postulate If the 3 sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. H Q R F P G

  4. ~ ~ Given: HF = HJ, FG = JK, H is the midpoint of GK. ~ Prove: Triangle FGH = Triangle JKH J F By the midpoint definition, GH = KH ∆FGH = ∆JKH by SSS. ~ K G H ~

  5. Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. F D B E C A

  6. From the information given, can you prove Triangle RED = Triangle CAT? Explain. ~ ~ R E Given: RE = CA, RD = CT, ‹R = ‹T C A ~ ~ T D No, cannot prove congruency. ∆CAT does not have the included angle between the two sides. Not SAS.

  7. From the information given, can you prove Triangle AEB = Triangle DBC? Explain. ~ ~ Given: EB = CB, AE = DB A B C By the definition of vertical angles, ‹ABE = ‹DBC. E ~ D No, cannot prove congruency. ∆AEB does not have the included angle between the two sides. Not SAS.

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