Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle that are congruent to two sides of another triangle, then the angle opposite the longer side of the first triangle is greater than the angle opposite the longer side of the second triangle.

Front

If triangle ABC has sides AB = 10 and AC = 12, and triangle DEF has sides DE = 10 and DF = 8, which angle is larger?

Back

Angle A is larger than Angle D because side AC (12) is longer than side DF (8).

Front

What can we conclude if two triangles have two sides equal and the third side of one triangle is longer than the third side of the other triangle?

Back

The angle opposite the longer side in the first triangle is greater than the angle opposite the longer side in the second triangle.

Front

If in triangle XYZ, XY = 5, XZ = 7, and in triangle PQR, PQ = 5, PR = 4, which angle is larger?

Back

Angle Z is larger than Angle R because side XZ (7) is longer than side PR (4).

Front

What is the relationship between the sides and angles in triangles according to the Hinge Theorem?

Back

In triangles, the larger the side, the larger the opposite angle.

Front

If angle A is greater than angle B in two triangles, what can we say about the sides opposite these angles?

Back

The side opposite angle A is longer than the side opposite angle B.

Front

In triangle ABC, if AB = 8, AC = 10, and in triangle DEF, DE = 8, DF = 6, which angle is larger?

Back

Angle C is larger than angle F because side AC (10) is longer than side DF (6).

Front

What does it mean if two triangles have two sides equal and the third side of one triangle is shorter?

Back

The angle opposite the shorter side is smaller than the angle opposite the longer side.

Front

If triangle GHI has GH = 9 and GI = 11, and triangle JKL has JK = 9 and JL = 10, which angle is larger?

Back

Angle I is larger than angle L because side GI (11) is longer than side JL (10).

Front

What is the conclusion if two triangles have two equal sides and the third side of one triangle is equal to the third side of the other triangle?

Back

The angles opposite the equal sides are also equal.