# Which Lengths make a Triangle? (2.1)

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 sketch. The purple and red sliders will be used to setup each problem. The sliders are correct for problem 1. Move the green point to determine the shortest and longest length of the third side so you don't have a triangle. Enter these numbers into the spreadsheet. You should get 3 for the shortest and 27 for the longest length. Now reset the sliders for problem 2. Find the shortest and longest lengths that don't create a triangle. Enter these lengths into your spreadsheet. Use the same steps for the remainder of the spreadsheet.

## Conjecture

Based on your investigation, how would you determine the shortest and longest lengths?

## Question 1

Two of the three sides of a triangle are 10 and 18. Based on your investigation, which side lengths won't work for the third side? (Select all of the lengths that don't work.)

## Question 2

Two of the three sides of a triangle are 17 and 23. Based on your investigation, which side lengths work for the third side? (Select all of the lengths that work.)

## Question 3

Two of the three sides of a triangle are 23 and 35. Based on your investigation, which side lengths work for the third side? (Select all of the lengths that work.)

Use this sketch to check your answers to the three questions. Make sure to set the sliders to the given lengths. Then move the orange point to look at all possible lengths for the third side. Did you select the correct answers to each question?

## Revised Conjecture (if needed)

Based on your investigation, how would you determine the shortest and longest lengths?

## Question 4

If two of the given lengths of a triangle are 23 and 54, the shortest length is 31 and the longest length is 77. Describe all of the lengths that work for the third side of the triangle?

## Question 5

If two of the lengths of a triangle are 62 and 80, describe all of the possible lengths for the third side of the triangle.