PYTHAGOREAN THEOREM

Brett Solberg AHS ‘11-’12

Warm-up

Simplify1) 2)

3) Solve for x 52 = x2 + 32

4) What is a hypotenuse?

Today’s Agenda

Test Review Pythagorean Theorem

find missing lengths in right triangles classify triangles

Converse prove triangles are right triangles

Test Review

5th

average 33.2/44 = 76% high 45

6th

average 33/44 = 75% high 45

Pythagorean Theorem

Pythagoras 500 BC Greece

Pythagoreans Devoted to Math Curious beliefs

Fallen Objects Transmigration Sacred Beans

“Knowledge is the greatest purification.”

Pythagorean Theorem

Pythagorean Theorem

The area of the square built upon the hypotenuse of a right triangles is equal to the sum of the areas of the squares upon the remaining sides.

Egypt 2600 BC

Babylon 1800 BC

China 600 BC

Pythagorean Theorem

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

Solving

Examples

Find the missing side lengths

Examples

Find the missing side lengths

Pythagorean Triples

A Pythagorean Triple is a set of non-zero whole numbers a, b, c in which a2 + b2 = c2

3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25

6, 8, 10 10, 24, 26 16, 30, 34 14, 48, 50

9, 12, 15 15, 36, 39 24, 45, 51 21, 72, 75

3x, 4x, 5x 5x, 12x, 13x 8x, 15x, 17x 7x, 24x, 25x

Example 2

Find b in the following right triangle. a = 7 b = ____ c = 25

Example 3

Is 4, 5, 6 a Pythagorean Triple?

Example 4

Find the distance from home base to 2nd base.

Converse

The Pythagorean Theorem If… Then…

The Converse of the Pythagorean Theorem If… Then…

Egyptian Rope Stretchers

Soccer Field Example

Example

Is the following a right triangle?

That value of x will make the triangle a right triangle?

Right/Obtuse/Acute Triangles If c2 = a2 + b2 the triangle is a right

triangle.

If c2 < a2 + b2 the triangle is an acute triangle.

If c2 > a2 + b2 the triangle is an obtuse triangle.

Example 5

Classify the triangles with the following side lengths

6, 11, 14

7, 8, 9

Homework

8.1 Worksheet and pg 420 # 2 – 16 even