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Geometry 5-7 Primer: The Hinge Theorem

Last updated about 4 years ago

5 Nsɛmmisa

Interact with the applet for a few minutes before responding to the item below.

10

For your convenience, the same applet is embedded below.

Set the applet such that m∠A ≠ m∠B and respond to the items that follow.

10

10

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3.

Extension: What conclusion(s) can you make about the relationship between the included angle measures and the third side lengths?

10

10

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1.

Explore: Which of the elements of the triangles in the applet can be modified? Which cannot be modified?

AB
BC
CA
DE
EF
FD
m∠A
m∠D
location of △ABC
location of △DEF

Can be modified
Cannot be modified

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2.

Exploration: In your current configuration, which angle has the greater measure?

A

D

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4.

Exploration: In your current configuration, which side length has the greater measure?

CB

FE

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5.

Extension: The properties you explored apply to all pairs of triangles with two sets of congruent sides and non-congruent included angles. This property is expressed in the Hinge Theorem. Fill in the blank to complete the theorem.
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the ? included angle.

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