Section 5.6 Inequalities in Two Triangles OBJECTIVE: To apply inequalities in two triangles BIG IDEA: Visualization ESSENTIAL UNDERSTANDING: In triangles that have two pairs of congruent sides, there is a relationship between the included angle and the third pair of sides. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

Hinge Theorem: If ____________ sides of one triangle are _______________ to two sides of another triangle, and the __________________ angles are not _______________, then the _______________ third side is ______________ the larger included angle. Converse of the Hinge Theorem: If ________ sides of one triangle are _______________ to two sides of another triangle, and the ________ sides are not ________________, then the larger _______________ angle is ____________ the longer third side. THEOREMS

EXAMPLE EX 1: Complete with <, > or = a) BC ________ EF b) JG ________ JI EXAMPLE

EX 1: Complete with <, > or = c) d) EXAMPLE

Ex 2: Match the conclusion on the right with the given information Ex 2: Match the conclusion on the right with the given information. Explain your thinking 1. A) 2. B) 3. C) 4. D) .

EX 3: Use an inequality to describe a restriction on the value of x as determined by the Hinge Theorem or its Converse a) b) EXAMPLE

5.6 p. 305 8 – 20 evens, 13, 19 9 questions