NAME
DATE
5-6
PERIOD
Enrichment
Hinge Theorem
The Hinge Theorem that you studied in this section states that if two sides of a
triangle are congruent to two sides of another triangle and the included angle in
one triangle has a greater measure than the included angle in the other, then the
third side of the first triangle is longer than the third side of the second triangle. In
this activity, you will investigate whether the converse, inverse and contrapositive
of the Hinge Theorem are also true.
X
Q
S
Y
1
2
Z
R
Hypothesis: XY = QR, YZ = RS, m∠1 > m∠2
Conclusion: XZ > QS
1. What is the converse of the Hinge Theorem?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Can you find any counterexamples to prove that the converse is false?
3. What is the inverse of the Hinge Theorem?
4. Can you find any counterexamples to prove that the inverse is false?
5. What is the contrapositive of the Hinge Theorem?
6. Can you find any counterexamples to prove that the contrapositive is false?
Chapter 5
42
Glencoe Geometry