7-5: Angle–Angle Triangle Similarity

Key Concept

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Triangle ABC within triangle AB′C′. The triangles share angle A. Angles B and B′ are congruent.

A ≅ ∠A and ∠ABC ≅ ∠AB′C′. So ΔABC ∼ ΔAB′C′.

Part 1

Example Justifying Two Triangles Are Similar Using Given Angles

Is ΔABC ∼ ΔDEF? Justify your reasoning.

Triangle ABC has angle A measuring 77° and angle B measuring 58°. Triangle DEF has angle E measuring 58° and angle F measuring 45°.

Solution

  • Method 1 Find the measure of ∠C.

    The sum of the measures of the interior angles of a triangle is 180°.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties