Converse of Pythagorean Theorem

1. 8-3 The Converse of the
Pythagorean Theorem
Objective
I can state and apply theorems to determine if a triangle is right,
obtuse, or acute.

2. 8-3 The Converse of the
Pythagorean Theorem
If the square of one side of a triangle is equal
to the sum of the squares of the other two
sides, then the triangle is a right triangle.
Is a triangle with lengths 20, 21, and 29
a right triangle?
In other words, is 292 = 202 + 212 ?
(Use the longest sides as your “c.”)

3. Pythagorean Triples
A Pythagorean triple consists of three
positive integers a, b, and c, such that
c2 = a2 + b2.
Some common triples (p. 295):
( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
or common multiples of these.

4. Theorem 8-3
If c2 = a2 + b2,
then mC = 90
and ΔABC is
right.
Theorem 8-4
If c2 < a2 + b2,
then mC < 90
and ΔABC is
acute.
Theorem 8-5
If c2 > a2 + b2,
then mC > 90
and ΔABC is
obtuse.
A B
C
ab
c
A B
C
a
b
c
A B
C
ab
c

5. Examples
A triangle has sides of the given lengths.
Is it acute, right or obtuse?
1. 5, 12, 14
2. 6, 7, 8
3.
4.

6. Solutions
142
? 122
+ 52
196 ? 144 + 25
196 > 169
obtuse
10
2
? 12 + 32
10 ? 1 + 9
10 = 10
right
5
2
? 3
2
+ 4
2
5 ? 3 + 4
5 < 7
acute
82
? 62
+ 72
64 ? 36 + 49
64 < 85
acute
1)
4)
2)
3)

7. Homework
• Pages 292-293 (Written Exercises)
• #2-30 evens
• Page 288-289 (Written Exercises)
• #19, 29, 32-38 evens