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SSS Inequality

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SSS Inequality

Study Guide

Key Definition

The SSS Inequality states that if two sides of one $\triangle$ are congruent to two sides of another $\triangle$, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.

Important Notes

If $BC > QR$, then $\angle A > \angle P$
If $BC < QR$, then $\angle A < \angle P$
SSS Inequality helps compare non-congruent sides
Useful in determining angle relationships
Applies to triangles with two pairs of congruent sides

Mathematical Notation

$\triangle$ represents a triangle

$\angle$ represents an angle

$\cong$ or $$\cong $$ means congruent

$>$ means greater than

$<$ means less than

Remember to use proper notation when solving problems

Why It Works

In a triangle, the larger side is opposite the larger angle; the SSS Inequality uses this relationship to compare the included angles when two sides are equal.

Remember

When comparing two triangles with two pairs of congruent sides, the triangle with the longer third side has the larger included angle.

Quick Reference

SSS Inequality:If two sides of $\triangle$ are congruent to two sides of another $\triangle$, the longer third side implies the greater included angle.

Understanding SSS Inequality

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In triangles with two pairs of equal sides, the one with the longer third side has the larger included angle.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

In two triangles, if $AB \cong PQ$ and $AC \cong PR$, and $BC > QR$, what can be concluded?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine two triangular routes where two legs are 4 km and 6 km in both. One route's closing side is 7 km, the other's is 5 km. Use the SSS Inequality to determine which closing track is longer.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given two triangles with sides of lengths 5 cm and 7 cm in both, and third sides 6 cm in one and 8 cm in the other, determine which triangle has the larger included angle between the congruent sides using SSS Inequality.

Challenge Quiz

Single Choice Quiz

Advanced

In two triangles, if two sides are congruent and the third side of one is longer, what can be inferred about the included angles?

Recap

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Review key concepts and takeaways