Is it a triangle, a right triangle, or not a triangle?

Objective and Goals

Target Objective:

Given three lengths of a triangle, students will determine whether the lengths create a right triangle by applying the Pythagorean Theorem and using a calculator.

Activity Goals:

Given three lengths, students will determine whether the lengths create any triangle by applying the Triangle Inequality Theorem.

Given three lengths, students will determine whether the lengths create a right triangle by applying the Pythagorean Theorem and using a calculator.

NYS Standards:

MST3.07.GE8.09: Students determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator.

Activity Five: Part One: Spaghetti Activity:

Directions: Take 3 or more pieces of spaghetti. Taking one piece at a time; break the spaghetti into 3 pieces (any way you want). Can you put the pieces together to create a triangle?

Using the other pieces, see what the measurements would be of a triangle that is also a right triangle. What would the measurements have to be to no make a triangle?

Try this with as many different pieces of spaghetti. What do you notice?

The Results:

Hopefully you found that when two sides put together are longer than the third side you get a triangle. The Triangle Inequality Theorem says that for all triangles two sides added together must be greater than the third side.

Example: If the pieces of spaghetti measured 2cm, 4cm and 5cm.

2 + 4 = 6 (which is greater than 5)

2 + 5 = 7 (which is greater than 4)

4 + 5 = 9 (which is greater than 2)

Activity Five: Part Two: Determining Right Triangles

The same idea works for part two, as it did for part one. The only exception is that you want to find a right triangle. In order to be a right triangle the three numbers need to work in Pythagorean Theorem.

a^2 + b^2 = c^2

Example 1: Let's pretend we have the sides 4inches, 5inches and 3 inches and we want to see if we have a right triangle. Plug the numbers into Pythagorean Theorem in number order .

a = 3 b = 4 c = 5

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

Example 2: Try the following: 12, 10, and 8.

a = 8 b = 10 c = 12

a^2 + b^2 = c^2

8^2 + 10^2 = 12^2

64 + 100 = 144

164 = 144? No. So, 8-10-12 is NOT a right triangle.

go back to Pythagorean Theorem

go back to Activity Four: Using Pythagorean Theorem to Solve Real World Problems

go on to Activity Six: Pythagorean Theorem Extra Practice