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Side-Angle-Side Similarity

Master side-angle-side similarity with interactive lessons and practice problems! Designed for students like you!

Understanding Side-Angle-Side Similarity

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Video explanation of this concept

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Beginner

Start here! Easy to understand

Beginner Explanation

If two triangles have a pair of congruent angles and the sides including those angles are proportional, then the triangles are similar: $\triangle ABC \sim \triangle DEF$
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Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice Quiz
Beginner

If $\angle A \cong \angle D$ and $\frac{AB}{DE} = \frac{AC}{DF}$, what can be concluded about $\triangle ABC$ and $\triangle DEF$?

Please select an answer for all 1 questions before checking your answers. 1 question remaining.
2

Real-World Problem

Question Exercise
Intermediate

Teenager Scenario

You want to create a scale model of a triangular garden. The original garden has an angle of $\angle ABC = 60^\circ$ and sides $AB = 10$ meters and $BC = 8$ meters. Your model will have $\angle DEF = 60^\circ$ and sides $DE = 5$ meters. What should the length of $EF$ be so that $\triangle ABC \sim \triangle DEF$?
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3

Thinking Challenge

Thinking Exercise
Intermediate

Think About This

A challenging problem involving $\triangle ABC$ and $\triangle PQR$ where $\angle A \cong \angle P$ and the sides including these angles are proportional (i.e., $\frac{AB}{PQ} = \frac{AC}{PR}$). Prove the similarity.

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4

Challenge Quiz

Single Choice Quiz
Advanced

Given $\triangle XYZ$ and $\triangle LMN$, if $\angle X \cong \angle L$, $XY = 3$, $XZ = 4.5$, $LM = 4$, and $LN = 6$. Are the triangles similar?

Please select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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