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Understanding Triangle Congruence: Identifying and Proving Congruent Figures

In this lesson, we explore the concepts of congruence in triangles, focusing on identifying congruent figures and their corresponding parts. Learn how to prove that two triangles are congruent through various methods, including the 3rd Angles Theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, the third angles must also be congruent. We will also cover properties of congruent triangles, such as reflexive, symmetric, and transitive properties, and practice constructing congruence statements.

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Understanding Triangle Congruence: Identifying and Proving Congruent Figures

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  1. 4.2 Congruence and Triangles Identify congruent figures and corresponding parts Prove that 2 triangles are congruent

  2. Congruence and Correspondence • When 2 figures are congruent there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

  3. Z • If Δ ABC is  to Δ XYZ, which angle is  to C?

  4. 3rd Angles Theorem • If two ’s of one triangle are  to two ’s of another triangle, then the third ’s are also .

  5. ARE THESE 2 TRIANGLES CONGRUENT?

  6. Example: find x ) ) 22o )) 87o )) (4x+15)o

  7. Example: Continued 22+87+4x+15=180 4x+15=71 4x=56 x=14

  8. Ex: ABCD is  to HGFE, find x and y. F E 9cm B (5y-12)o A 91o 86o H G 113o 4x-3cm D C 4x-3=9 5y-12=113 4x=12 5y=125 x=3 y=25

  9. Properties of Congruent Triangles(Theorem 4.4) 1. Reflexive: 2. Symmetric: 3.Transitive:

  10. Writing a Congruence Statement D C A B F E

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