Hinge Theorem Worksheet

Explore the Hinge Theorem (SAS Inequality) and its converse with this worksheet for Grade 9 geometry students. Includes multiple choice, true/false, fill-in-the-blank, and short answer questions.

Grade 9 Math GeometryHinge Theorem

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Includes

Multiple ChoiceTrue / FalseFill in the BlanksShort Answer

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10

Topics

Hinge TheoremSAS InequalityGeometryTrianglesInequalities

6 sections · Free to use · Printable

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Hinge Theorem Worksheet

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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.

1. In two triangles, if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is:

shorter than the third side of the second triangle.

longer than the third side of the second triangle.

congruent to the third side of the second triangle.

cannot be determined.

2. Which of the following theorems is also known as the SAS Inequality Theorem?

Triangle Inequality Theorem

Hinge Theorem

SSS Inequality Theorem

Pythagorean Theorem

3. 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.

True

False

4. If two sides of a triangle are 5 cm and 7 cm, and the included angle is 60 degrees, and another triangle has two sides 5 cm and 7 cm with an included angle of 50 degrees, then the third side of the first triangle is shorter.

True

False

5. The Hinge Theorem compares the lengths of the third sides of two triangles when two sides are and the included angles are .

6. In triangles ABC and DEF, if AB = DE, BC = EF, and m∠B > m∠E, then AC DF.

7. Consider two triangles, ΔXYZ and ΔPQR. If XY = PQ = 8 units, YZ = QR = 10 units, and m∠Y = 70°, while m∠Q = 60°, which third side is longer, XZ or PR? Justify your answer using the Hinge Theorem.

8. Given two triangles with two pairs of congruent sides, if the third side of the first triangle is 15 cm and the third side of the second triangle is 12 cm, what can you conclude about the included angles of the two triangles? Explain your reasoning using the Converse of the Hinge Theorem.