Congruency Proving

This lesson is an extension of the introductory course on Congruency and Similarity – An Introduction. In the introductory course, you learned what congruent and similar triangles are.

In this lesson, you will learn how to prove that two triangles are congruent.

Related Lessons:
  1. S3 Similarity Proving
  2. S3 Similar Solids

Proving Congruency

When proving that two triangles are congruent, we can use the following criteria:

  • SSS
  • SAS
  • SAA
  • ASA
  • RHS

Note that RHS is used specifically for right-angled triangles. If a triangle is right-angled, it is usually best to try using RHS first, unless it cannot be applied.

Proving Congruency Example 1

In the diagram, ∠𝐴𝐸𝐷=∠𝐴𝐢𝐡=90° and AE=AC.

  1. Name a pair of congruent triangles and state the reason.
  2. If ∠𝐢𝐴𝐸=35°, find ∠CPD

Proving Congruency Example 2

  1. In the diagram ACX and YBC are straight lines. It is given that AB=AC=CX and YB=BC. Showing your working clearly, prove that two triangles are congruent.
  2. State the angle which has the same value as βˆ πΆπ΅π‘‹
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Related Lessons:

  1. S3 Similarity Proving
  2. S3 Similar Solids

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