# UNIT 4 LESSON 1: TRIANGLE INEQUALITIES

- Author:
- Rachel Turner, Terry Lee Lindenmuth, ohoward, kbailey

- Topic:
- Inequalities

Given ΔGHJ, complete the following statements. The included angle of sides JG and GH is angle ________

Angle H is the opposite angle to side _______.

The side opposite to ∠J is side _____.

## ANGLE MEASURE AND SIDE LENGTH RELATIONSHIPS

## ANGLE MEASURE AND SIDE LENGTH RELATIONSHIPS

1. When is the largest angle, which side is the longest?

2. When is the smallest angle, which side is the shortest?

3. When side c is the longest, which angle is the biggest?

4. What is the relationship between between the angles and the side lengths for a triangle?

## PRACTICE

What is the order of the angles from largest to smallest?

## EXAMPLE

Triangle ABC is shown in the diagram. The lengths of the sides are in terms of the variable *n*, where *n* ≥ 4. Choose the correct inequality:

## CONVERSE OF THE TRIANGLE PARTS RELATIONSHIP THEOREM

## REAL WORLD CONNECTION

## REAL WORLD CONNECTION

1. The converse of the triangle parts theorem tells us that the side that's opposite of the largest angle will be the _________ side 2. Therefore, ______ has the longer distance to hike back to the car.

Michael and Jacob are standing on two docks that are 20 miles apart. They are watching a ship that is out in the ocean. The angle between the dock and the line connecting Michael and the ship is 48°, and the angle between the other dock and the line connecting Jacob and the ship is 37°. If the ship can travel to either dock, which dock would be closest? Explain your answer.