# Which Lengths make a Triangle? (2.1)

- Author:
- Roger Gemberling

**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.)

**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.