THE PYTHAGOREAN THEOREM AND AREA OF A

TRIANGLE

Warm – Up!! Good Morning! As you walk in, get your calculator and pick up your guided notes from the podium. Go ahead and label your triangle based on the definitions below (be sure to fill in the definitions too!):Hypotenuse – the side of a right triangle opposite the right angle and the longest side.Legs – the sides of a right triangle that are not the hypotenuse.

THE PYTHAGOREAN THEOREM

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.

IF I AM GIVEN 2 SIDES OF A RIGHT TRIANGLE MAKE UP THE SIDES OF

PYTHAGOREAN TRIPLE, HOW DO YOU FIND THE MISSING SIDE?

There are 2 possible scenarios:1. You are given both legs of the right triangle and

need to solve for the hypotenuse.

2. You are given one leg and one hypotenuse and need to solve for the other leg.

EXAMPLE 1: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE.

222 cba 6 8 x²

36 + 64 = x²

100= x²2100 x x10

EXAMPLE 2: USE THE PYTHAGOREAN THEOREM TO FIND THE HYPOTENUSE.

PYTHAGOREAN TRIPLES

A Pythagorean Triple is a set of 3 positive integers or whole numbers that satisfies the Pythagorean theorem.

IS IT A PYTHAGOREAN TRIPLE? 3, 4, and 5

21, 28, and 35

30, 72, and 91

14, 48, and 50

252525169543 222

yes

yes

no

yes

EXAMPLE 3: FIND THE MISSING LEG

222 cba x 3 5²

x²+ 9 = 25

x² = 16162 x 4x

YOU TRY!! FIND THE MISSING LEG

FIND THE AREA WHEN GIVEN A LEG AND THE HYPOTENUSE

1. Find the other leg by plugging the known values into the Pythagorean Theorem.

2. Use the 2 legs in the formula for area of a triangle A = ½BH

Find the perimeter of a triangle by adding the

sides. P = a + b + c, where a, b, and c

are sides Example:

FIND THE AREA OF THE TRIANGLE

What is the formula for the area of a triangle?

A = ½bh

How will we find the height?222 135 h

16925 2 h1442 h 12h

bhA21

)12)(10(21

60

Find the Area of the Triangle

222 124 h14416 2 h

1282 h

28h

bhA21

)28)(8(21

232

YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE.

816

YOU TRY!! FIND THE AREA WHEN GIVEN A LEG AND A HYPOTENUSE.

1317