Algebra 1 Common Core Student Edition, Grade 8-9

Object ives To solve problems using the Pythagorean Theorem

To identify right triangles

Get t i n g Read y

The diagram shows three square

house lots th a t b o rd er a pond

shaped like a rig h t trian gle.

W h a t is t h e a r e a o f e a c h house

lo t? Can you w rite an equation to

relate all three areas? Explain.

This is alm ost like

an optical illusion.

What do you see,

th r e e squares or

th r e e sid es o f a

trian gle?

MATHEMATICAL

PRACTICES

The Pythagorean

Theorem

@ Common Core State Standards

G-SRT.C.8 Use trig o n o m e tric ratios and the

Pythagorean Theorem to solve rig h t triangles in applied

problems.

MP 1, MP 2, MP3, MP4

Lesso n
Vocabulary
hypotenuse
leg
Pythagorean
Theorem
conditional
hypothesis
conclusion
converse

There are special names for the sides of a right triangle like

the one in the Solve It. The side opposite the right angle is the

hypotenuse. It is the longest side. Each of the sides forming the

right angle is a leg. The Pythagorean Theorem, named after the

Greek mathematician Pythagoras, relates the lengths of the legs

and the length of the hypotenuse.

Essent ial Und er st and ing The lengths of the sides of a right triangle have a

special relationship. If you know the lengths of any two of the sides, you can find the

length of the third side.

Theor em The Pythagorean Theorem

Words

In any right triangle, the sum of the squares of the

lengths of the legs is equal to the square of the length of

the hypotenuse.

Algebra

a2 + b2 = c2

Ch ap t er 10 Rad i c al Ex p r e ssi o n s a n d Eq u a t i o n s