Hinge Theorem Worksheet

Hinge Theorem Worksheet

Read each question carefully and provide the best answer. Show all your work where applicable.

1. In ΔABC and ΔDEF, if AB = DE, BC = EF, and m∠B > m∠E, which of the following is true?

2. 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 triangle, then the   side of the first triangle is longer than the corresponding side of the second triangle.

3. If two sides of ΔXYZ are congruent to two sides of ΔUVW, and XZ > UW, then the measure of the included angle ∠Y is   than the measure of the included angle ∠V.

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 larger than the included angle of the second triangle.

5. Consider two triangles, ΔPQR and ΔSTU. If PQ = ST, QR = TU, and PR = 10 cm while SU = 12 cm, what can you conclude about the relationship between m∠Q and m∠T? Justify your answer using a theorem.

6. In the diagram below, AB = DE and BC = EF. If m∠B = (3x + 10)° and m∠E = (2x + 30)°, and AC < DF, find the possible range of values for x.

7. Two gates are built such that the lengths of their sides are fixed. Gate 1 has sides of 8 ft and 10 ft, with the angle between them being 70°. Gate 2 has sides of 8 ft and 10 ft, with the angle between them being 60°. Which gate requires a longer diagonal brace?