Download 5.6 Inequalities in Two Triangles and Indirect Proof

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Transcript
Bell Problem
List the sides and angles in order from smallest to
largest.
5.6 Inequalities in Two Triangles
Standards:
1. Develop mathematical arguments and
proofs
2. Use types of reasoning/methods of proof
Hinge Theorem
If two sides of one triangle are congruent to two sides of
another triangle, and the included angle of the first is larger
than the included angles of the second, then the third sides of
the first is longer than the third side of the second.
Converse of the Hinge Theorem
If two sides of one triangle are congruent to two sides of
another triangle, and the third side of the first is longer than
the third side of the second, then the included angle of the
first is larger than the included angle of the second.
Ex. Given that ST ≅ PR, how does <PST compare to
<SPR?
Ex. Use the diagram.
a. If PR = PS and m<QPR > m<QPS, which is longer, SQ
or RQ?
a. If PR = PS and RQ < SQ, which is larger, <RPQ or
<SPQ?
Ex. Copy and complete with <, >, or =.
Ex. Write and solve an inequality to describe a restriction on
the value of x.
Homework
5.6 Practice B worksheet