# Lesson 2.3.1 - continuation

- Author:
- Roger Gemberling

In this sketch, you will explore the range of possible lengths for a triangle when two of the side lengths are given. You have ten problems to explore in this activity. The

**purple**and**red**sliders will be used to setup each problem. The sliders are correct for problem 1. When you move the**green point**, there are a lot of triangles being created. What is the shortest and longest length so the third segment (**blue segment**) so you**DON'T**have a triangle. Enter these numbers into the spreadsheet. Now reset the**purple**and**red**sliders for the next problem in spreadsheet. Find the shortest and longest length so the third segment**create a triangle. Enter these lengths into your spreadsheet. Use the same steps for the remainder of the spreadsheet.****DOESN'T**## Conjecture

Based on this investigation, how would you determine the shortest and longest lengths that DON'T work?

## Question 1

Two of the three sides of a triangle are 10 and 18. Which side lengths won't work for the third side of the triangle? (Select all of the lengths that don't work.)

## Question 2

Two of the three sides of a triangle are 17 and 23. Which side lengths work for the third side of the triangle? Select all of the lengths that work if 17 and 23 are two of the side lengths.

## Question 3

Two of the three sides of a triangle are 23 and 35. Which side lengths work for the third side of the triangle? Select all of the lengths that work if 23 and 35 are two of the lengths.