The AAS Rule
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 24 of 63.
Two angles fix the third, because the three angles of a triangle add up to 180°. So if two angles of one triangle equal two angles of another, the third angles are equal too, and any matching side pair gives you ASA in disguise. This is AAS: two pairs of angles and a pair of sides that is not between them.
| Statement | Reason |
|---|---|
| 1. ∠CAB = ∠FDE | Given |
| 2. ∠ABC = ∠DEF | Given |
| 3. CA = FD | Given |
| 4. △ABC ≅ △DEF | AAS, using lines 1, 2 and 3 |
The arcs are at A and B, but the ticked side CA does not join them. The board tells ASA and AAS apart: pick ASA here and it says these parts prove it by AAS.
Challenge
The marks show ∠G = ∠M, ∠H = ∠N, and HK = NO. Prove that △GHK ≅ △MNO, 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