pythagorean theorem ppt blog
TRANSCRIPT
Pythagorean Theorem
Parts of a Right Triangle
b
ca
Hypotenuse
Right Triangle
Leg
Leg
b
ca
Use the sides of the triangle to make a square with equal sides.
35
4
55
5
4
4
4
3
3
3
a = 3b = 4c = 5
Find the area of each of the squares created…
Side = 3Area = 32 = 9
Side = 4Area = 42 = 16
Side = 5Area = 52 = 25
b
ca9
16
25
What is the relationship between the area of the 2 smaller squares and the area of the larger square?
Discovery Activity
We can conclude that the sum of the area of the 2 smaller squares is equal to the area of the larger square.
9 16 25+ =
Pythagorean Theorem
Years ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) and you made a square on each of the three sides, then ... the biggest square had the exact same area as the other two squares put together!
Pythagorean Theorem is: a2 + b2 = c2
What Pythagoras Discovered!!!
Pythagorean Theorem
Problems in this unit will not include square shapes but will look like this! b
c ___ + ___ = ____a
Although you do not see the square shapes you will still need to square the sides of the triangle to determine the relationship.
a2 b2 c2
Pythagorean Theorem
3
4
5
1.) Plug in values of a, b, & c into the formula.
2.) Square values of a, b, c
3.) Add the squares on the left side.
The left and right sides should be equal!
a2 + b2 = c2 __2 + __2 = __2
__ + __ = ____ = __
3 4 5
9 16 25
25 25
Why is this useful?
• If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)
Let’s try!!!a
b
?
Example 1
5 12
25 144
169
169
13
Example 2
9 15
81 225
81
144
144
12
Now You Try!!!
Know Before You Go
Today’s Lesson was on:___________________
Three important things to remember:1.) Write the formula for the Pythagorean Theorem.2.) What is the only type of triangle that the
Pythagorean Theorem will work for?3.) Why is the Pythagorean Theorem useful?