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SAS Congruence Visualization

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About This Diagram

This side-by-side comparison demonstrates why the included angle matters in triangle congruence proofs. It contrasts valid SAS with the ambiguous SSA case.

Side-by-Side Comparison

Left Side: Valid SAS

  • Two sides and their included angle are congruent
  • The angle is BETWEEN the two marked sides
  • This guarantees triangle congruence

Right Side: Invalid SSA

  • Two sides and a non-included angle are marked
  • The angle is NOT between the marked sides
  • Two different triangles can have the same SSA measurements!

Key Concept: Included Angle

Included angle: The angle formed BY the two sides being compared.

  • In SAS: ∠B is between sides AB and BC
  • In SSA: ∠C is NOT between sides AB and AC

SAS Congruence 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 triangles are congruent.

Warning About SSA

SSA (Side-Side-Angle with a non-included angle) is NOT a valid congruence criterion because the same SSA measurements can produce two different triangles.

Interaction

Click on either panel to focus on it. Click again to show both panels.

Learning Objectives

  • Identify the included angle in SAS
  • Apply SAS congruence correctly
  • Analyze why SSA fails as a congruence criterion

Bloom's Taxonomy Level

Understanding, Applying, and Analyzing

Iframe Embed Code

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