Learning Target #3
Solve for missing sides of a right triangle using the Pythagorean Theorem and Pythagorean triples
1
Explain why most manhole covers are round and not square/rectangular.
2
Pythagorean Theorem
2
2
a + b = c
2
A
c
b
C
B
a
If ABC is a right triangle, then a
2
+ b 2 = c
2
Converse of P.T.:
If a 2 + b 2 = c 2, then ABC is a right Δ
3
Pythagorean Triples
­positive integers that satisfy the P.T.
ex: 3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
{
and all of their multiples
ex: Find the missing side
12
35
17
12
4
The twin skyscraper Petronas towers in Kuala Lumpur, Malaysia 5
23.26 m
47.57 m
x
Find the length of the support beams.
6
ASSIGNMENT
p. 538 #7­15
7
Learning Target #4
Determine if a triangle is right
8
ex: Find the area of the triangle to the nearest tenth of a meter
7 m
7 m
h
10 m
9
Applying the Converse of the P.T.
ex: The triangles below appear to be right triangles. Tell whether they are right triangles or not.
4 √95
15
36
8
7
√113
10
*If a
*If a
2
+ b 2 > c 2, then ΔABC is acute.
2
+ b 2 < c 2, then ΔABC is obtuse.
ex: Classify the triangle as right, acute or obtuse by the given side lengths.
a. 38, 77, 86
b. 10.5, 36.5, 37.5
11
ASSIGNMENT
p. 538 #25, 26, 29
p. 546 #11­16, 18­21
12
c
3 mi.
9%
x
13
Chapter 9 L.T. #4 Ramp Design (work with a partner)
14