Which of the following sets of numbers can be the lengths of the sides of a triangle? 0.7, 1.4, 2.1 4, 5, 10 4 , 6 , 20 12.3, 13.9, 25.2 Problem of the Day

Section 5-6 Inequalities in Two Triangles

Then Now Objectives You recognized and applied properties of inequalities to the relationships between the angles and sides of a triangle. Apply the Hinge Theorem or its converse to make comparisons in two triangles.

Common Core State Standards Content Standards G.CO.10 – Prove theorems about triangles. Mathematical Practices 1) Make sense of problems and persevere in solving them. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Inequalities in Two Triangles

Compare JK and MQ. Example 1

Compare m∠SRT and m∠VRT. Example 1

Compare the given measures. m∠STR and m∠TRU PQ and RQ Example 1

Two groups of skiers leave from the same lodge Two groups of skiers leave from the same lodge. Group A goes 4 miles due east and then turns 70° north of east goes 3 miles. Group B goes 4 miles due west and then turns 75° north of west and goes 3 miles. At this point which group is FARTHER from the lodge? Explain your reasoning. Example 2

Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain the back area. Titus can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which leg can Titus raise higher above the table? Example 2

Find the range of possible values for x. Example 3*

Find the range of possible values for x. Example 3*

Find the range of possible values for x. Example 3*

p.375 #1 – 4, 10 – 16, 21, 22, 47 – 49 Homework

Complete each statement with the correct symbol: > < = AB ____ BK ST ____ SR m∠CDF ____ m∠EDF m∠R ____ m∠T Problem of the Day