Missing Side Lengths

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

Now that you have learned the Pythagorean Theorem, you will need to apply it to solve math questions.

Visual 1: Two right triangles are given.

Question 1: Use the Visual to...

Find the missing side length of each right triangle.[br][list=1][*]a = 7, b = 10, [color=#ff7700][b]c = ?[/b][/color][/*][*]a = 5, b = 13, [color=#ff7700][b]c = ?[/b][/color][/*][/list][b][color=#ff7700]Hint:[/color][/b] Use the [b][color=#6aa84f]Pythagorean Theorem[/color][/b].

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.[br][list=1][*][b][color=#ff7700]a = ?[/color][/b], b = 6, c = 8[/*][*]a = 3, [b][color=#ff7700]b = ?[/color][/b], c = 11[/*][/list]What is different about these triangles compared to the triangles in Question 1? How does this difference change the math process?[br][br][b][color=#ff7700]Hint:[/color][/b] Use the [b][color=#6aa84f]Pythagorean Theorem[/color][/b].

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.[br][list=1][*] a = ?, b = ?, c = ?[/*][*] a = ?, b = ?, c = ?[/*][/list]How can you tell which side lengths are a, b, and c?[br][br]Hint: Use the [b][color=#6aa84f]Pythagorean Theorem[/color][/b].

Question 3: Check your answer.

Visual 4: Two triangles are given.

Question 4: Use the Visual to...

Think about it.[br][br]Could you use the [b][color=#6aa84f]Pythagorean Theorem[/color][/b] to find the missing sides of these two triangles?[br][br]Why or why not?[br][br][b][color=#ff7700]Hint:[/color][/b] 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 [color=#6aa84f][b]Pythagorean Theorem[/b][/color] (or not), and find the angle measurements.[br][list=1][*]Side lengths: 5, 5, ~7.07[/*][*]Side lengths: 5, 5, ~8.94[/*][*]Side lengths: 5, 5, ~4.47[/*][/list]If a triangle follows the [color=#6aa84f][b]Pythagorean Theorem[/b][/color], what does it have?[br][br]How can you tell if a triangle is a right triangle (or not) without looking at it?