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# sss Inequality

If we understand the properties of SSS inequality, we can solve many triangles more easily. Let''s find out how:

## The definition of SSS inequality

The Hinge Theorem helps us understand the relationship between the side lengths and included angles of two triangles when two pairs of corresponding sides are congruent. It states that:

If two sides of one triangle are congruent to the two sides of a second triangle, and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle must be longer than the third side of the second triangle.

Conversely, if two sides of one triangle are congruent to the two sides of a second triangle, and the included angle of the first triangle is smaller than the included angle of the second triangle, then the third side of the first triangle must be shorter than the third side of the second triangle.

Consider two triangles, ΔABC and ΔPQR, with the following congruent sides:

AB ≅ PQ
and
AC ≅ PR
.

If
∠A > ∠P, then BC > QR
(Case 1)

If
∠A

∠P, then BC

QR

(Case 2)

The Hinge Theorem is useful in solving problems where we need to compare the lengths of the non-congruent sides of two triangles when we know the corresponding sides and the included angles. By using the theorem, we can establish the relationship between the side lengths and draw conclusions accordingly.

Triangles

SAS Inequality

Congruent Angles

## Flashcards covering the sss Inequality

Basic Geometry Flashcards

Common Core: High School - Geometry Flashcards

## Practice tests covering the sss Inequality

Common Core: High School - Geometry Diagnostic Tests

Intermediate Geometry Diagnostic Tests

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