According to the Hinge Theorem, if the included angle in the first triangle is larger, which statement is true about the third sides?

According to the Hinge Theorem, if the included angle in the first triangle is larger, which statement is true about the third sides?

• A. The third side of the first triangle is longer
• B. The third side of the second triangle is longer
• C. The two third sides are equal
• D. Not enough information to compare third sides

Answer: (A)

This tests the Hinge Theorem: when two triangles have two pairs of sides equal and the included angle between those sides is larger in one triangle, the third side opposite that angle is longer in that triangle. Since the first triangle has the larger included angle, its third side must be longer than the third side of the second triangle. So the statement that the third side of the first triangle is longer is the correct one.

This tests the Hinge Theorem: when two triangles have two pairs of sides equal and the included angle between those sides is larger in one triangle, the third side opposite that angle is longer in that triangle. Since the first triangle has the larger included angle, its third side must be longer than the third side of the second triangle. So the statement that the third side of the first triangle is longer is the correct one.