SAS Similarity

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 56 of 63.

The last similarity rule mirrors SAS. If two sides of one triangle are in the same ratio as two sides of another, and the angles between them are equal, the triangles are similar: SAS similarity. Its line cites the equal angles; the side lengths come from the figure.

$Triangles ABC and DEF: AB = 5, CA = 4, DE = 15, FD = 12, with the angles at A and D marked equal$

Statement	Reason
1. ∠BAC = ∠EDF	Given
2. △ABC ∼ △DEF	SAS similarity, using line 1

Check both parts: 15/5 = 3 and 12/4 = 3, so the ratios match, and the marked angles at A and D sit between those sides. With the angle anywhere else, the rule would not apply, just as SSA proves nothing for congruence.