Why SSA Fails

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 19 of 63.

What if the angle is not between the two sides? That arrangement is side side angle, SSA, and it does not prove anything. The figure shows why.

$Triangles ABC and ABD share AB and the angle at A, with BC equal to BD$

△ABC and △ABD share the side AB and the angle at A, and BC = BD. That is two sides and an angle in both, yet the triangles are clearly different: one is far smaller. The side BC swings like a gate around B and can close onto the line at two points. The angle at A is not between AB and BC, so nothing stops the swing.

Proofs have no SSA rule. If you cite two sides and an angle that is not between them, the board refuses the step and tells you so.

Challenge

△ABC has side AB, side BC and the angle at A. The point P moves on the circle around B, so BP always equals BC. Drag P onto the line AX at a new point, not at C. Then press Check.

Try it yourself

$Drag the figure and watch$

Drag the figure and watch

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape Matching Sides Matching Angles What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs