Pythagorean Theorem and Converse

The Pythagorean Theorem and Its Converse

Objective: Use the Pythagorean Theorem and Its Converse.

Using the Pythagorean Theorem

In the Pythagorean Theorem, "c" ALWAYS stands for the HYPOTENUSE of the right triangle- the side across from the right angle.

"a" and "b" stand for the other two sides- the LEGS which create the right triangle.

The HYPOTENUSE is always the longest side length!

Multiple Choice

Is the missing side of the right triangle a leg or the hypotenuse?

• hypotenuse

• leg

• I don't know

Multiple Choice

Is the missing side of the right triangle a leg or the hypotenuse?

• hypotenuse

• leg

• I don't know

Multiple Choice

Is the missing side of the right triangle a leg or the hypotenuse?

• hypotenuse

• leg

• I don't know

How to Use the Pythagorean Theorem

* Is the missing side the hypotenuse or one of the legs of the right triangle?

* Plug your values into the equation.

* DON'T FORGET TO TAKE THE SQUARE ROOT AS THE LAST STEP IN SOLVING THE EQUATION!

* Round your answer to the nearest tenth (one decimal place) or leave in simplest radical form(depending on directions)

Multiple Choice

Find the length of the missing side.

• 15.3

• 10.2

• 21

• 4.6

Multiple Choice

Find the length of the missing side.

• 11.4

• 5.7

• 4.1

• 112

Multiple Choice

Find the length of the missing side.

• 35.7

• 36

• 23

• 23.8

Multiple Choice

A 31-foot support wire is attached from the top of a 25-foot tall telephone pole to a point on the ground. How far from the base of the pole does the wire meet the ground?

[Hint: Draw a picture to help you set this one up!]

• 7.5 feet

• 39.8 feet

• 17.5 feet

• 18.3 feet

Pythagorean Theorem Converse

​Here are some examples!

• Examples A and B ARE right triangles because the three values make the equation work!

• Examples C & D are NOT right triangles because the values do not make the equation true!

• Don't forget! The hypotenuse is always the longest side!

Multiple Choice

Do these side lengths represent a right triangle?

a² + b² = c²

18, 24, 30

• NO

  36 + 48 ≠ 60

• YES

  324 + 576 = 900

• I don't know

Multiple Choice

Do these side lengths represent a right triangle?

a² + b² = c²

31, 35, 39

• NO

  961 + 1225 ≠ 1521

• YES

  961 + 1225 = 1521

• I don't know

Multiple Choice

Do these side lengths represent a right triangle?

a² + b² = c²

15, 16, 21

• NO

  225 + 256 ≠ 441

• YES

  225 + 256 = 441

• I don't know