Warm UP - Simply
5 36
225
−2 75
8
6
800
3 32
8.2 – Pythagorean Theorem
Learning Target 1: to be able to simplify radicals.
Learning Target 2: to be able to apply and use the Pythagorean
Theorem.
Perfect Squares…
1•1 = 1
5 • 5 = 25
9 • 9 = 81
2•2 = 4
6 • 6 = 36
10 • 10 = 100
3•3 = 9
7 • 7 = 49
11 • 11 = 121
4 • 4 = 16
8 • 8 = 64
12 • 12 = 144
Pythagorean Theorem
c
a
hypotenuse
leg
b
leg
2
2
a +b = c
Hint: ALWAYS locate the hypotenuse first!!!
2
Pythagorean Theorem
15
6
11
x
x
9
Pythagorean Theorem
x
7.2
5.3
x
8
12
Common Pythagorean Triplets
3,4,5
6 , 8 , 10
9 , 12 , 15
5,12,13
What kind of triangle am I?
Determine whether each set of numbers can be the measures
of the sides of a triangle. If so classify as acute, obtuse, or
right.
9, 40, 41
7, 14, 16
5, 5, 8
4, 4, 5
The bottom of a ladder is placed 12 feet from a wall. The
ladder reaches 16 feet above the ground to touch the wall.
How long is the ladder?
The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12
feet long. How far above the ground does the ladder touch the wall?
An isosceles triangle has congruent sides of 20 cm. The base is 10
cm. Find the height of the triangle.
Super Stumper
You use four stakes and string
to mark the foundation of a
house. You want to make
sure the foundation is
rectangular.
A friend measures the four
sides to be 30 feet, 30 feet, 72
feet, and 72 feet. Opposite
sides are congruent. He says
these measurements prove
the foundation is rectangular.
Is he correct? Why or why
not?
72 ft
30 ft
30 ft
72 ft
You measure the diagonal to be 78 feet. How does this
help prove if the figure is a rectangle?
72 ft
30 ft
30 ft
72 ft
What’s Wrong??
http://www.youtube.com/watch?v=DUCZXn9RZ9s
“The sum of the square roots of any two sides of an
isosceles triangle is equal to the square root of the
remaining side.”
~The Scarecrow
Homework
Pg. 546
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