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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, ______ .

Select all that apply
  • A
  • B
  • C
Check my answer (3)

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, _____ .

Select all that apply
  • A
  • B
  • C
Check my answer (3)

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, _____ .

Select all that apply
  • A
  • B
  • C
Check my answer (3)

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 ________.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Question 2:

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

The above triangle is _______.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Question 3:

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

The above triangle is _______.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

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