Missing Side Lengths

Author:: Tamara Willis

Topic:: Pythagoras or Pythagorean Theorem

Learning Goal

Students will learn how to use the Pythagorean Theorem to find missing side lengths of right triangles and to determine if a triangle is a right triangle or not.

The Pythagorean Theorem

Visual 1: Two right triangles are given.

Question 1: Use the Visual to...

Find the missing side length of each right triangle.

a = 7, b = 10, c = ?
a = 5, b = 13, c = ?

Hint: Use the Pythagorean Theorem.

Question 1: Check your answer.

Visual 2: Two right triangles are given.

Question 2: Use the Visual to...

Find the missing side length of each right triangle.

a = ?, b = 6, c = 8
a = 3, b = ?, c = 11

What is different about these triangles compared to the triangles in Question 1? How does this difference change the math process? Hint: Use the Pythagorean Theorem.

Question 2: Check your answer.

Visual 3: Two right triangles are given.

Question 3: Use the Visual to...

Find the missing side lengths of each right triangle.

a = ?, b = ?, c = ?
a = ?, b = ?, c = ?

How can you tell which side lengths are a, b, and c? Hint: Use the Pythagorean Theorem.

Question 3: Check your answer.

Visual 4: Two triangles are given.

Question 4: Use the Visual to...

Think about it. Could you use the Pythagorean Theorem to find the missing sides of these two triangles? Why or why not? Hint: Notice what is different about these two triangles compared to the triangles from the previous questions.

Question 4: Check your answer.

Visual 5: Click and drag the points to explore relationships between the sides of the triangle and the areas of the squares.

Question 5: Use the Visual to...

Determine if each triangle follows the Pythagorean Theorem (or not), and find the angle measurements.

Side lengths: 5, 5, ~7.07
Side lengths: 5, 5, ~8.94
Side lengths: 5, 5, ~4.47

If a triangle follows the Pythagorean Theorem, what does it have? How can you tell if a triangle is a right triangle (or not) without looking at it?