Chasing in Isosceles Shapes
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 51 of 63.
The isosceles rules also help you find sizes. When ticks mark two equal sides, one base angle gives the other, and the angle sum gives the apex. An outside angle on the extended base gives a base angle through a linear pair.
Here the outside angle at C is 130°, so ∠ACB = 50° (angles on a straight line). The ticks make ∠ABC = 50° too. The apex is then 180 - 50 - 50 = 80°. The Isosceles triangle rule can also jump straight from one base angle to the apex, since the two base angles together with the apex make 180°.
Challenge
In △KLM the ticks show KL = KM, and the base LM is extended to N. The outside angle at M is 112°. Find the apex angle ∠LKM, then press Check.
Try it yourself
Find the marked part of the figure
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