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G-CO.10 Warmup M2-034-A06-V01

Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.

Use the converse of the isosceles triangle theorem to conclude two sides are equal

Problem

Use the converse of the isosceles triangle theorem. If angle \(B\) equals angle \(C\) in triangle \(ABC\), what can you conclude?

Unworked triangle configuration showing only the supplied givens. Open full size
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What this problem is really about

This is the converse direction of the isosceles theorem: equal angles tell us about their opposite sides. We’ll match each marked angle to the only side that does not touch its vertex, then state the resulting side congruence without involving the shared base.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-CO.10
Category
Geometry
Domain
Congruence
Objective
Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.
Problem type
Use the converse of the isosceles triangle theorem to conclude two sides are equal