Problem preview

G-GMD.6 Warmup M2-040-A10-V03

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

Use the hinge theorem informally to compare third sides or included angles in two triangles

Problem

\(\text{Two}~\text{triangles}\) have \(\text{two}~\text{pairs}~\text{of}~\text{equal}~\text{corresponding}~\text{adjacent}~\text{sides}\), and their opposite third sides measure \(12\) and \(15\). Apply the converse hinge theorem to identify the triangle with the larger included angle and state the side-to-angle comparison.

Answer choices

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Both triangles have the same included angle.

There is not enough information to tell.

The triangle with opposite side 15 has the larger included angle.

The triangle with opposite side 12 has the larger included angle.

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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: Use the hinge theorem informally to compare third sides or included angles in two triangles