Hinge Theorem Worksheet

Hinge Theorem Worksheet

Read each question carefully and apply the Hinge Theorem or its converse to determine the correct answer. Show all your work for full credit.

1. In ΔABC and ΔDEF, AB = DE, BC = EF. If m∠B > m∠E, what can you conclude about the lengths of AC and DF?

2. Given ΔPQR and ΔXYZ, PQ = XY, QR = YZ. If PR < XZ, what can you conclude about the measures of ∠Q and ∠Y?

3. The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is   than the third side of the second triangle.

4. The Converse of the Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is   than the included angle of the second.

5. In ΔABC, AB = 10, BC = 12. In ΔDEF, DE = 10, EF = 12. If AC = 15 and DF = 14, which of the following is true?

6. Two triangles have two pairs of congruent sides. The included angle of the first triangle measures 70 degrees, and the included angle of the second triangle measures 65 degrees. What can you say about the lengths of their third sides?