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

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

(Case 2)∠P, then BC

QR

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.

Common Core: High School - Geometry Flashcards

Common Core: High School - Geometry Diagnostic Tests

Intermediate Geometry Diagnostic Tests

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