# Converse of the Pythagorean Theorem

- Author:
- Michelle Stafford, Mr.Hajel, Vicki O'Malley

## Explore the Converse of the Pythagorean Theorem

Your goal is to use the manipulative below to explore and understand the Converse of the Pythagorean Theorem and its corollaries. Recall: a corollary is something that is easily proven from something else. The Pythagorean Theorem can be used for more than just right triangles. Who knew?

## Before you begin:

The Pythagorean Theorem states: "If you have a right triangle, then ". What should the converse of this statement be? Write it out in one complete conditional statement.

## Step 1:

Using the sliders in the manipulative above, create a right triangle, compute the values and and record these values in the google doc below. You will record all future values here, so keep the google doc open.

## Record your values here:

https://docs.google.com/spreadsheets/d/1NDY7pzbdz8PTeMIjnkC8jQA2qu78sVJ-XaTErwV4-Q0/copy
Copy and paste the above link to another tab in your browser.

## What do you notice?

Fill in the blank: When you have a **right** triangle, ______ .

## Step 2:

Now, using the same manipulative as in step 1, use the sliders to create three different acute triangles. Note the a, b, and c values in your google spreadsheet and then compute the and values.

## What do you notice?

Fill in the blank: When you have an **acute** triangle, _____ .

## Step 3:

Now, using the same manipulative as in step 1, use the sliders to create three different obtuse triangles. Note the a, b, and c values in your google spreadsheet and then compute the and values.

## What do you notice?

Fill in the blank: When you have an **obtuse** triangle, _____ .

## Apply What You've Learned:

Use the relationships you recognized above to classify the following triangles.

## Question 1:

Classify the triangle above as right, obtuse, or acute. Show all work in the box below. You may use a^2 to represent .

The above triangle is ________.

## Question 2:

Classify the triangle above as right, obtuse, or acute. Show all work in the box below.

The above triangle is _______.

## Question 3:

Classify the triangle above as right, obtuse, or acute. Show all work in the box below.

The above triangle is _______.