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G-GMD.6 Warmup M2-040-A03-V01

Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.

Order triangle sides from angle measures

Problem

A triangle has angle measures \(A=40^{\circ}\), \(B=60^{\circ}\), \(C=80^{\circ}\). Order the sides from shortest to longest.

Triangle A B C with angles A 40 degrees, B 60 degrees, and C 80 degrees. Open full size
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What this problem is really about

Angle order transfers to side order only after each angle is paired with the side directly across from it. We’ll rank the angles, map each vertex to the side that does not contain that vertex, and then use larger-angle-opposite-longer-side to transfer the ordering without relying on shared letters.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GMD.6
Category
Geometry
Domain
Geometric Measurement and Dimension
Objective
Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Problem type
Order triangle sides from angle measures