Intro to Pythagorus

​Searching for the Right Pattern

​A right triangle is a triangle with a right angle. A right angle has a measure of 90^o and is indicated by a square drawn at the corner formed by the angle.

​Let's find a pattern.

​Let's find a pattern. Did anyone find a pattern?

Let's do this. Let's find squares. (Calculator)

Let's do this. Let's find squares. (Calculator)

Open Ended

Write what you noticed about the right triangles and their patterns.

Open Ended

In the right triangle shown, the lengths of the sides are

a, b, and c.

Using the pattern you discovered in the previous activity, what statement can you make about the relationship among

a², b², and c²

Multiple Choice

Which side length must be longer?

• A

• B

• C

Multiple Choice

True or False

(Think about it)

The SUM of the two shorter sides of a triangle are longer than the longest side.

• True

• False

The side opposite the right angle in a right triangle is called the hypotenuse. The other two sides are called legs of the right triangle. In the figure, the sides with lengths a and b are the legs, and the side with length c is the hypotenuse.

​a and b are the legs

c is the hypotenuse

Hotspot

Identify the location of the hypotenuse.

Hotspot

Identify the location of the legs.

Pythagorean Theorem

The special relationship that exists between the squares of the lengths of the sides of a right triangle is known as the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse.

​a² + b² = c²

You can verify that the Pythagorean Theorem holds true for the triangles in the previous activity.

Multiple Choice

Verify that the Pythagorean Theorem holds true.

A right triangle with the side lengths of 8, 15, and 17.

• True

• False

Multiple Choice

Verify that the Pythagorean Theorem holds true.

A right triangle with the side lengths of 7, 24, and 25.

• True

• False

Exit Ticket

Multiple Choice

Which measurements could represent the side lengths in feet of a right triangle?

• 10ft, 24 ft, 26 ft

• 14 ft, 14 ft, 14 ft

• 3 ft, 3 ft, 18 ft

• 2 ft, 3 ft, 5 ft