The SAS Rule
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 17 of 63.
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.
| 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
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Congruence & Proof
1What a Proof Is
Given and ProveStatements and ReasonsChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons2Congruent Triangles
Same Size, Same ShapeMatching SidesMatching AnglesWhat Congruence GivesRecap: Matching Parts8Proofs with Vertical Angles
Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles