Problem preview

G-CO.10 Warmup M2-034-A10-V01

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

Classify a segment using the median definition

Problem

Classify the segment as median, not median, or insufficient evidence: triangle \(ABC\); segment \(AM\); \(M\) is stated midpoint of \(BC\).

Triangle ABC with M marked as the midpoint of side BC and segment AM drawn.

Big Picture

What this problem is really about

A triangle segment is classified by where it begins and ends, not by how it looks. We’ll check that one endpoint is a vertex and the other is the midpoint of the opposite side, use the equal base pieces as evidence, and then apply the definition.

Answer choices

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Preview only

AM is a median because AB = AC.

AM is not a median because BM and MC are unequal.

There is insufficient evidence because M may not be the midpoint of BC.

AM is a median because M is the midpoint of opposite side BC.

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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: Classify a segment using the median definition