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G-CO.10 Warmup M2-034-A05-V01

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

Find specified angles in an isosceles triangle

Problem

Find every named missing angle for triangle \(ABC\) with \(AB=AC\) and \(m\angle~B=48°\).

Isosceles triangle ABC with equal sides AB and AC marked and base angle B labeled 48°; angles A and C are unknown. Open full size
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What this problem is really about

Equal sides determine equal opposite angles, so the first task is matching each marked side to the angle across from it. We’ll transfer the known base-angle measure to its partner and then use the triangle sum to recover the remaining vertex angle.

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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
Find specified angles in an isosceles triangle