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The Pythagorean Theorem
Tutorial 12d
The Pythagorean Theorem
In a right triangle, the side opposite the
right angle is the longest side. It is the
hypotenuse.
The other two sides are the legs of a right
triangle.
a
c
b
Side c is the hypotenuse,
and is the longest side.
Sides a and b are the legs
of the triangle.
Pythagorean Theorem
In a right triangle, the sum of the
squares of the lengths of the legs is
equal to the square of the length of
the hypotenuse.
a=3
c =5
b =4
a2 + b2 = c2
Example:
32 +
42 = 52
Example #1
2.
1.
18in
c
34in
a2 + b2 = c2
182 + 342 = c2
324 + 1156 = c2
1480 = c2
1480  c
38  c
100m
70m
c
3.
35ft
c
a2 + b2 = c2
702 + 1002 = c2
4900+10,000 = c2
1,4900 = c2
14900  c
122  c
68ft
a2 + b2 = c2
352 + 682 = c2
1225+4624 = c2
5,849 = c2
5849  c
76  c
Example #2
Find the value of the variable. Round your answers to the nearest tenth.
a2 + b2 = c2
x2 + 42 = 62
x2 + 16 = 36
-16 -16
x2 = 20
x  20
x  4.5
a2 + b2 = c2
102 + y2 = 142
100 + y2 = 196
-100
-100
y2 = 96
y  96
y  9.8
a2 + b2 = c2
92 + p2 = 102
81+ p2 = 100
-81
-81
p2 = 19
p  19
p  4.4
Pythagorean Theorem
When the lengths of the sides of a right
triangle are integers, the integers form a
Pythagorean triple.
Example:
5
3
32 + 4 2 = 5 2
9 + 16 = 25
25 = 25
4
The numbers 3, 4, & 5 are called Pythagorean Triples
The Converse of the
Pythagorean Theorem
If the square of the length of one side of
a triangle is equal to the sum of the
squares of the lengths of the other two
sides, then the triangle is a right triangle.
Is this triangle a right triangle?
10
6
8
62 + 82 = 102
36 + 64 = 100
100 = 100
Yes it is a right triangle
More Examples
Are the following triangles right triangles?
1.
2.
7.52 + 42 ? 8.52
152 + 72
56.25 +16 ? 72.25 225 +49
? 72.25 No, 274
Yes, 72.25 =
it is a right triangle
3.
? 172
? 289
? 289
it is not a right triangle
122 + 182 ? 212
144 +324 ? 441
? 441
No, 468 
it is not a right triangle