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AA (Angle-Angle) Similarity

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AA (Angle-Angle) Similarity

Study Guide

Key Definition

If two pairs of corresponding angles in two triangles are congruent, then the triangles are similar. This is known as $AA (\text{Angle-Angle})$ Similarity.

Important Notes

Similar figures have the same shape but may be different in size.
Congruent figures are the same size and shape.
If two pairs of corresponding angles are congruent, then all three pairs of corresponding angles are congruent due to the Angle Sum Theorem.

Mathematical Notation

$\angle A \cong \angle P$ means angle A is congruent to angle P

$\triangle ABC \sim \triangle PQR$ means triangle ABC is similar to triangle PQR

The symbol $\sim$ is used for similarity and $\cong$ is used for congruence.

Why It Works

AA Similarity is a consequence of the Angle Sum Theorem. Since the sum of angles in a triangle is always 180°, if two pairs of angles are congruent, the third pair must also be congruent.

Remember

$\angle A \cong \angle P$ and $\angle B \cong \angle Q$ implies $\triangle ABC \sim \triangle PQR$

Quick Reference

AA Similarity:$\triangle ABC \sim \triangle PQR$ if $\angle A \cong \angle P$ and $\angle B \cong \angle Q$

Understanding AA (Angle-Angle) Similarity

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Video explanation of this concept

Beginner

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Beginner Explanation

If two pairs of corresponding angles in two triangles are equal, then the triangles are similar. This is called AA Similarity.

Practice Problems

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Quick Quiz

Single Choice Quiz

Beginner

If $\angle A \cong \angle P$ and $\angle B \cong \angle Q$, are $\triangle ABC \sim \triangle PQR$?

Real-World Problem

Question Exercise

Intermediate

Architectural Scenario

An architect is building a smaller model of a skyscraper. The bases of both the skyscraper and its model are triangular. If their corresponding angles are equal, can we say the triangular bases are similar?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given $\angle A \cong \angle P$ and $\angle B \cong \angle Q$, are $\triangle ABC \sim \triangle PQR$?

Challenge Quiz

Single Choice Quiz

Advanced

Given the vertex correspondence X→Z, Y→W, and Z→X, and if $\angle X \cong \angle Z$ and $\angle Y \cong \angle W$, are $\triangle XYZ \sim \triangle ZWX$?

Recap

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