5.6 Hinge Theorem

The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than the included angle of the other, then the side opposite the larger angle is longer than the side opposite the smaller angle.

By comparing the angles opposite the sides in two triangles with two equal sides. The side opposite the larger angle is longer.

Side BC is longer than side AC.

In triangles, larger angles are opposite longer sides.

The third side of the triangle with the larger included angle is longer.

Side EF is the longest.

If two triangles have two sides of equal length and the side opposite the larger angle is longer, then the included angle of that triangle is larger.

Identify the two triangles, compare the lengths of the equal sides, and analyze the included angles to determine the relationship between the opposite sides.

Determining which of two ramps is steeper based on their angles and lengths.

The side opposite angle 1 is longer.