All the squares below are made of gold. You have your choice of the larger pink one, or you can take the two smaller ones together. Which option would you choose?

Find the area of the triangle.

4 in

5 in

7.2: The Pythagorean Theorem and Its Converse

Objective: The use the Pythagorean Theorem and its converse

PYTHAGOREAN THEOREM

MUST be used on a right trianglec is the hypotenuse, a and b are the legs of

the right triangle

a2 + b2 = c2

Pythagorean Triple

3 INTEGERS that satisfy the Pythagorean Theorem

Some Common Examples:3, 4 and 5 (and multiples of)5, 12 and 137, 24 and 25

Examples

1. a.) Find x.b.) Do the side lengths form a Pythagorean Triple?

2. Find x.

25

x

10

126

x

Find x. Simplify the radical.

9x

15

Theorems:

1. If a2 + b2 = c2, the triangle is a right triangle.

2. If a2 + b2 < c2, the triangle is obtuse.

3. If a2 + b2 > c2, the triangle is acute.

A triangle has the following side lengths. Is it a right triangle?

1. 16, 48,50

2. 84, 85, 13

Classify the triangles as obtuse, acute or right.

1. 6, 11 , 14

2. 15,25,20

3. 9, 8, 7

On graph paper…

• Draw a rectangle with the dimensions 4 inches by 5 inches.

• Calculate the length of the diagonal without using a ruler.

• Once you have your answer, measure the diagonal and compare results.

A baseball diamond is a square with 90 ft sides. Home plate and second base are opposite vertices of the square. About how far is home plate from second base?

Classwork Problems1. Find x. Leave your answer in simplest radical form.

2. Find the missing side of the triangle. Round your answer to the nearest tenth.

3. State if the 3 side lengths form a right triangle: 7, 4 ,

4. State if each triangle is acute, obtuse or right:

a.) 6, 14, 9

b.) 12, 16, 20

7

x

15

18

x15

33