Hinge Theorem Worksheet
This worksheet focuses on applying the Hinge Theorem and its converse to compare side lengths and angle measures in triangles.
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Hinge Theorem Worksheet
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Read each question carefully and apply the Hinge Theorem or its converse to solve the problems. Show all your work.
1. In \(\triangle ABC\) and \(\triangle DEF\), if \(AB = DE\), \(BC = EF\), and \(m\angle B > m\angle E\), what can you conclude about \(AC\) and \(DF\)?
\(AC < DF\)
\(AC > DF\)
\(AC = DF\)
Cannot be determined
2. Consider two triangles, \(\triangle PQR\) and \(\triangle XYZ\). If \(PQ = XY = 8\) cm, \(PR = XZ = 10\) cm, and \(QR = 12\) cm while \(YZ = 11\) cm. Compare the measures of \(\angle P\) and \(\angle X\). Justify your answer.
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 than the included angle of the second triangle, 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 triangle, then the included angle of the first triangle is smaller than the included angle of the second triangle.
True
False
5. In \(\triangle ABC\), \(AB = 7\) and \(BC = 10\). In \(\triangle XYZ\), \(XY = 7\) and \(YZ = 10\). If \(AC = 13\) and \(XZ = 15\), compare the measures of \(\angle B\) and \(\angle Y\).
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