Equal Angles, Equal Sides
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 48 of 63.
The base angles theorem also runs backwards. If two angles of a triangle are equal, the sides opposite them are equal, and the triangle is isosceles. In a proof the reason is Sides opposite equal angles, citing the line with the equal angles.
Here the arcs say ∠ABC = ∠ACB. The side opposite ∠ABC is AC, and the side opposite ∠ACB is AB, so AB = AC. A triangle with two equal sides is isosceles, which is the Definition of isosceles. Be careful which sides you pair: each equal angle faces the side across from it, not the side it touches. On a find or reason board the same rule is called Isosceles triangle sides.
Challenge
In △PQR the angles at Q and R are marked equal. The sides PQ and PR are highlighted. Pick the rule that makes them equal, then press Check.
Try it yourself
Name the rule that links them
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 Reasons7Using CPCTC
Congruent, Then EqualProving a BisectorFlowchart ProofsProving a MidpointRecap: Using CPCTC10Isosceles Triangle Proofs
Base Angles in a ProofEqual Angles, Equal SidesProving IsoscelesThe Perpendicular BisectorChasing in Isosceles ShapesRecap: Isosceles Proofs2Congruent 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