Chapter 5 Section 7Inequalities in Two

Triangles

Objectives Students will be able to apply

inequalities in two triangles

Essential Understanding In triangles that have two pairs of

congruent sides, there is a relationship between the included angle the third pair of sides

When you close a door, does the angle between the door and frame (at the hinge) get bigger or smaller?

The Hinge Theorem (SAS Inequality 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 larger included angle

Using the Hinge Theorem What inequality relates LN and OQ?

Using the Hinge Theorem In ΔABC AB = 3, BC = 4, and CA = 6 In ΔPQR, PQ = 3, QR = 5, and RP = 6 How can you use indirect reasoning

to explain why m<P > m<A?

Applying the Hinge Theorem

The picture shows a pair of scissors in two different positions. In which is the distance between the tips of the two blades greater? Justify your answer.

Converse of the Hinge Theorem If two sides of one triangle are

congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side.

What is the range of possible values for x?

First find the upper limit for the value of x by writing an inequality

Second find the lower limit for the value of x by writing an inequality. Remember an angle has to be greater than zero

Write the final answer as an inequality of the possible values

Find the range of possible values for x

Using the Converse of the Hinge Theorem

What is the range of possible values for x?

Upper limit? Lower Limit?

Writing a Proof Given: <MON = 80, O is the midpoint

of LN Prove: LM > MN

Writing a Proof

Homework Pg. 336 # 6 – 15, 23 11 problems