1. 7-2 The Pythagorean Theorem
3/2/17
7-2 The Pythagorean Theorem
Objective: To use the Pythagorean Theorem and its converse.
THEOREM PYTHAGOREAN THEOREM
In a right triangle, the sum of the squares of the length of
the legs is equal to the square of the length of the hypotenuse
a2 + b2 = c2
PYTHAGOREAN TRIPLE: a set of nonzero whole numbers a, b, and c that satisfy the equation a2 + b2 = c2
Examples of triples on next slide…. c a b

2. Are these Pyth. Triples?: 1) 20, 21, 29 2) 12, 16, 25
Ex: 3, 4, , 12, 13
7, 24, , 15, 17
Are these Pyth. Triples?: 1) 20, 21, 29
2) 12, 16, 25
Ex: Find x. Leave answer in simplified radical form.
a2 + b2 = c Pythagorean Theorem
82 + x2 = Substitution
64 + x2 = Simplify
x2 = Subtract x
x = Take Square Root
x = 16• Simplify
x =
= 841 yes!
≠ 625 nooo!

3. Ex: Find the area of the triangle 12 m 12 m 102 + h2 = 122 h
Find h, then use it to find Area
Ex: Find the area of the triangle m m
102 + h2 = h
100 + h2 = 144
h2 = m m
h = h
h = 4•
h =
A = ½ bh where b = 20, h = 2 11
= ½ (20)(2 11)
= m2
Since we knew all three sides already, Heron’s formula could have also been used.

4. THEOREM 7-5 CONVERSE OF THE PYTHAGOREAN
If the square of the length of one side is equal to the sum of the squares of the length of the other two sides, then the triangle is a right triangle.
Ex: Is this a right triangle?
c2 = a2 + b
852 =
7225 =
7225 = YES
Is this? 16, 48, 50
≠ 2500 Nooo!

5. THEOREM 7-6
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse.
If c2 > a2 + b2, the triangle
is obtuse! c a b

6. THEOREM 7-7
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute.
If c2 < a2 + b2, the triangle is acute! a c
Ex: Acute, obtuse, or right? b
6, 11, 14
142 =
196 =
196 > OBTUSE since c2 > a2 + b2
12, 13, 15
152 =
225 =
225 < 313 ACUTE since c2 < a2 + b2

7. 100 > 25 + 64 therefore it’s obtuse
Find x. Answer in simplest radical form. 1) x 12 2) x
3) Find the area of the triangle. Leave answer in simplest radical form.
11 in in
20 in
4) The lengths of the sides of a triangle are 5 cm, 8 cm, and 10 cm. Is it acute, right or obtuse?
= x2
225 = x2
x = 15
64 + x2 = 196
x2 = x = 4•33
x =
100 + h2 = 121
h2 = 21
h = 21
A = ½(20)( 21)
A =
100 > therefore it’s obtuse

8. Assignment: Page 360 #1 – 9, 16 – 26