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SSS (Side-Side-Side) Postulate

Master SSS (Side-Side-Side) Postulate with interactive lessons and practice problems! Designed for students like you! NOTE: Several practice problems below are missing the side–length data for the second triangle in each pair. Without those numbers, students cannot actually apply S-S-S. See the in-line comments in the practice-problem text.

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SSS (Side-Side-Side) Postulate

Study Guide

Key Definition

The SSS Postulate states: If one $\triangle$'s three sides are congruent to another $\triangle$'s three sides, then these two triangles are congruent, i.e., $\triangle ABC \cong \triangle DEF$.

Important Notes

The symbol $\cong$ represents congruence.
Congruence means the figures have the same size and shape.
$\overline{AB} \cong \overline{DE}$ implies equality in length.
SSS is a fundamental postulate in geometry for proving triangle congruence.
Remember to verify all three pairs of sides when using SSS.

Mathematical Notation

$\triangle$ represents a triangle

$\cong$ means congruent

$\overline{AB}$ stands for line segment AB

$\angle$ represents an angle

$\sqrt{x}$ represents the square root of x

Remember to use proper notation when solving problems

Why It Works

The SSS Postulate works because if all three sides of one $\triangle$ are equal to all three sides of another $\triangle$, then the two triangles must be identical in size and shape.

(Consider expanding this section with a short rigid-motion argument or a reference to Euclid I.8 so students understand *why* only side data suffices.)

Remember

SSS stands for Side-Side-Side, which is a tool to test triangle congruence using side lengths.

Quick Reference

SSS Postulate:$\overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, \overline{CA} \cong \overline{FD} \Rightarrow \triangle ABC \cong \triangle DEF$

Understanding SSS (Side-Side-Side) Postulate

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The SSS Postulate is simple: if three sides of one $\triangle$ match three sides of another, the triangles are congruent.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which pair of triangles are congruent by SSS Postulate?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine building two identical triangular frames. Verify congruency using SSS: $\overline{AB} = 5ft, \overline{BC} = 7ft, \overline{CA} = 9ft; \overline{DE} = 5ft, \overline{EF} = 7ft, \overline{FD} = 9ft$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given $\triangle XYZ$ and $\triangle UVW$ with sides $\overline{XY} = 6, \overline{YZ} = 8, \overline{ZX} = 10; \overline{UV} = 6, \overline{VW} = 8, \overline{WU} = 10$, determine if they are congruent.

Challenge Quiz

Single Choice Quiz

Advanced

Determine which triangles are congruent using SSS in a complex setup.

Recap

Watch & Learn

Review key concepts and takeaways