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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

In SAS similarity, if one angle of a triangle is congruent to one angle of another triangle and the sides including those angles are proportional, then the triangles are similar. For example, in triangles ABC and DEF, if ∠A ≅ ∠D and AB/DE = AC/DF = k for some constant k, then triangle ABC is similar to triangle DEF. Corresponding angles are equal and corresponding sides are in proportion.
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Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice Quiz
Beginner

Which pair of triangles are similar by SAS? $\angle A \cong \angle D$ and $\frac{AB}{DE} = \frac{AC}{DF}$.

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 need to determine if two triangles for a skateboard ramp are similar. Triangle ABC has ∠B = 30°, side AB = 5 ft, and BC = 8 ft. Triangle DEF has ∠E = 30°, DE = 10 ft, and EF = 16 ft. Determine if these triangles are similar using the SAS criterion.
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3

Thinking Challenge

Thinking Exercise
Intermediate

Think About This

Determine if $\triangle XYZ$ is similar to $\triangle PQR$ using SAS. Triangle XYZ has ∠X = 50°, XY = 6 cm, XZ = 9 cm. Triangle PQR has ∠P = 50°, PQ = 12 cm, PR = 18 cm.

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4

Challenge Quiz

Single Choice Quiz
Advanced

In the triangles $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$ and $\frac{AB}{DE} = \frac{BC}{EF}$. Are they 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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