6th Grade Math Textbook, Progress

In about 500 B.C., Pythagoras, a Greek mathematician,

proved that a certain pattern exists in all right triangles.

A right triangle has a 90° angle. The side

opposite the 90° angle is called the hypotenuse.

The remaining sides are called legs.

Pythagorean Theorem

In a right triangle, the sum of the

squares of the lengths of the legs,

aand b, is equal to the square of

the length of the hypotenuse, c.

a^2 
b^2 c^2

When you know the lengths of any two sides of

a right triangle, use the Pythagorean Theorem

to find the length of the third side.

Pythagorean Theorem

Find the length of the hypotenuse of

a right triangle whose legs measure

6 cm and 8 cm.

a^2 
b^2 c^2

62 
 82 c^2

36 
 64 c^2

100 c^2


 100 c

10 c

So the hypotenuse is 10 cm long.

The length of the hypotenuse of a right

triangle is 17 ft. If the length of one leg

is 15 ft, find the length of the other leg.

a^2 
b^2 c^2

152 
b^2  172

225 
b^2  289

225 
b^2  225  289  225

b^2  64

b
 64 

b 8

So the other leg is 8 ft long.

Substitute the

given values of

the variables.

Solve for c.

a^2 
b^2 c^2

32 
 42  52

Substitute the

given values of

the variables.

Solve for b.

Find the length of the missing side of each right triangle.

1. legs: 10 cm 2. legs: 9 in. 3. legs:
   24 cm in. 12 m
   hypotenuse: 15 in. hypotenuse: 13 m

?

4. The diagonal of a rectangle is 15 mm.
   If the length of the rectangle is 12 mm,
   what is the width?
   5. Raul walks 30 m north and then
   16 m east. How far is he from the
   starting point?

leg a

b leg

c hypotenuse

a

b

c^3

4

5

? m

hypotenuse ? cm

8206-2_409 10/12/07 6:52 PM Page 409