Unit 6 Lesson 5 Inequalities in Two Triangles CCSS G-CO 10: Prove theorems about triangles. G-SRT 5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Lesson Goals Use the Hinge Theorem and its converse to compare side lengths and angle measures. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

DE F AB C Theorem Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, but the angles between the sides have different measures, then the lengths of the third sides of each triangle compare the same as the measures of the angles. >=<?>=<?>=<?>=<?>=<?

Theorem Hinge Theorem Converse If two sides of one triangle are congruent to two sides of another triangle, but the third sides have different lengths, then the measures of the angles between the first two sides compare the same as the lengths of the third sides. DE F >=<?>=<?>=<?>=<?>=<? AB C

Example 45 o 58 o 60 o 11 in A C B 15 in D F E 58 o

Example o X Y Z 9 in R Q P 40 o

Example

Dusty leaves an airport and flies 200 miles due west. He then changes direction and flies S 60 o W for 90 miles. Ripslinger leaves the airport and flies 200 miles due east. He then changes direction and flies N 15 o E for 90 miles. Both Dusty and Ripslinger have flown 290 miles, but which plane is farther from the airport? airport 60 o 15 o 120 o 165 o ? < Dusty Ripslinger Ripslinger is farther because the angle between the congruent sides is larger.

Summary Explain the Hinge Theorem/Converse in your own words. Give a real life example of the Hinge Theorem (Do not use flying from the airport or your elbow – come up with your own example) and explain why it is an example of the Hinge Theorem/Converse.

p 305: 7 – 20, 28, 29