The SAS Rule

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 14 of 60.

Two sides and the angle between them fix a triangle too. Lay down one side, turn through the angle, lay down the other side: the two free ends are now fixed, and so is the third side joining them. This is SAS, side angle side.

$Triangles ABC and DEF: ticks on AB, DE and on CA, FD, arcs at A and D$

Statement	Reason
1. AB = DE	Given
2. CA = FD	Given
3. ∠CAB = ∠FDE	Given
4. △ABC ≅ △DEF	SAS, using lines 1, 2 and 3

The A in SAS sits between the two S letters on purpose: the angle must be the included angle of the two sides. Here AB and CA meet at A, and the arcs are at A and D, so SAS applies.

Challenge

The marks show KL = XY, LM = YZ and ∠KLM = ∠XYZ. The two side lines are written. Add the angle line and the congruence, then press Check.

Try it yourself

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape 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