Download Warm up: Find the missing length. Use the Pythagorean Theorem a2

Warm up:
Find the missing length. Use the Pythagorean Theorem­­
a2 +b2 =c2
(leg)2 + (leg)2 = (hypotenuse)2
OBJECTIVES:
•use the Pythagorean Theorem
•use the converse of the Pythagorean Theorem
Section 7­2 ____________________
1. a = 5, b = 12
2. a = 6, b= 8
Pythagorean Theorem ­­In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.
B
3. a = 15, b = 15
a2 + b2 = c2
c
a
A
4. a = 14, b = 27
Example 1:Dryden is located at 117 degrees longitude and 34 degrees latitude. Ames is located at 122 degrees longitude and 37 degrees latitude. Find the degree distance to the nearest tenth between Dryden and Ames.
b
C
Example 2: Find x.
7 in.
14 in.
x in.
1
Converse of the Pythagorean Theorem
­­If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.
Example 3: Verify that PQR is a right triangle.
P( 3, 2) Q(­3, 6) R(5, 5)
If a2 + b2 = c2, then ABC is a right triangle.
Pythagorean Triple ­­
Guided Practice:
Example 4: Determine whether each set of measures can be the sides of a right triangle. Then determine whether it is a Pythagorean Triple.
1. Find the Error. Maria and Conchita are determining whether 5, 12, 13 is a Pythagorean Triple. Who is correct and why?
Maria
Conchita
132 + 52 = 122
52 + 122 = 132
169 + 25 = 144
25 + 144 = 169
193 = 144
169 = 169
NO
YES
a. 8, 15, 16
b. 20, 48, 52
c. 3 , 6 , 3 5 5 5
2
Find x.
2. 3.
4
7
x
5. Determine whether JKL with vertices J(­2, 2), K(­1, 6) and L(3, 5) is a right triangle. Explain.
10
6
5
7
x
4.
x
37.5
20
Determine whether each set of numbers can be the measure of the sides of a right triangle. Then state whether they form a Pythagorean Triple.
geometric mean ­­
5. 15, 36, 39 7. 40, 20, 21
The geometric mean is the positive number x where the proportions a : x = x : b is true. a = x x b
so x2 = ab OR x = ab
6. 44, 8, 108
3
Do you have any Vocab questions?
OBJECTIVES:
IN CLASS: p. 354 ­ 356
# 12 ­ 29, 40, 60, 62 ­ 70 even
HOMEWORK: Notes and Check for Understanding 7­3
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