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7.1 – Apply the Pythagorean Theorem
In your group, do the following:
1. Find the area of one of the four right triangles
b
a
a
b
b a
c
1
2A bh
1
2A ab
In your group, do the following:
2. Find the TOTAL area for all four right triangles
b
a
a
b
b a
c
14
2ab
2
2ab
In your group, do the following:
3. Find the area of the tilted square
b
a
a
b
b a
c
A = s2
A = c2
In your group, do the following:
4. Find the area of the large square
b
a
a
b
b a
c
A = s2
A = (a+b)2
A = (a+b)(a + b)
A = a2 + 2ab + b2
In your group, do the following:
5. Write an equation to show the area of the tilted square plus the four triangles equal the area of the large square and simplify
b
a
a
b
b a
c
c2 + 2ab = a2 + 2ab + b2
c2 = a2 + b2
Sound familiar?
Pythagorean Theorem:
leg
leg
hypotenusea
b
c
c2 = a2 + b2
(hypotenuse)2 = (leg)2 + (leg)2
If a triangle is a right triangle, then (hypotenuse)2 = (leg)2 + (leg)2
1. Find the value of x.
c2 = a2 + b2
x2 = 152 + 362
x2 = 225 + 1296
x2 = 1521
x = 39
H
1. Find the value of x.
c2 = a2 + b2
x2 = 42 + 92
x2 = 16 + 81
x2 = 97
97x
H
1. Find the value of x.
c2 = a2 + b2
x2 = 62 + 32
x2 = 36 + 9
x2 = 45
53x
H
1. Find the value of x. c2 = a2 + b2
172 = x2 + 82
289 = x2 + 64
225 = x2
x15
H
1. Find the value of x. c2 = a2 + b2
272 = x2 + 92
729 = x2 + 81
648 = x2
x218H
1. Find the value of x. c2 = a2 + b2
422 = x2 + 362
1764 = x2 + 1296
468 = x2
x136
H
2. Find the area of the isosceles triangle.c2 = a2 + b2
102 = h2 + 82
100 = h2 + 64
36 = h2
x6
8 8
bhA2
1
1(16)(6)
2A
8
48A in2
HH
2. Find the area of the isosceles triangle.c2 = a2 + b2
122 = h2 + 42
144 = h2 + 16
128 = h2
bhA2
1
1(8)(8 2)
2A
4
32 2A
h28
cm2
H
2. Find the area of the isosceles triangle.c2 = a2 + b2
442 = h2 + 242
1936 = h2 + 576
1360 = h2
bhA2
1
1(48)(4 85)
2A
24
96 85A
h854
m2
24 24
H
7.2 – Converse of the Pythagorean
Pythagorean Theorem Converse:
If c2 = a2 + b2, then the triangle is a right triangle
a
b
c
Acute Triangle:
If c2 < a2 + b2, then the triangle is acute
a
b
c
Obtuse Triangle:
If c2 > a2 + b2, then the triangle is obtuse
a
b
c
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
c2 = a2 + b2
172 = 82 + 152
289 = 64 + 225
289 = 289
8 + 15 > 17
8 + 17 > 15
15 + 17 > 8
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
a. 8, 15, 17
3 + 4 > 9
b. 3, 4, 9
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
7 > 9
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
c2 = a2 + b2
196 = 100 + 121
196 221
c.
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
10, 11, 14
10 + 11 > 14
10 + 14 > 11
11 + 14 > 10
142 = 102 + 112
<
c2 = a2 + b2
61 = 25 + 36
61 = 61
d. 2 2 261 5 6
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
5, 6, 61
61 7.8
5 + 6 > 7.8
5 + 7.8 > 6
6 + 7.8 > 5
12 ,10 ,13 c2 = a2 + b2
144 = 13 + 100
144 113
e.
222 101312
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
13 3.6
3.6 + 10 > 12
3.6 + 12 > 10
10 + 12 > 3.6
>
c2 = a2 + b2
37.21 = 18.49 + 27.04
37.21 45.53
f. 4.3, 5.2, 6.1 2 2 26.1 4.3 5.2
For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!
Triangle: YES or NO ACUTE, RIGHT, or OBTUSE
4.3 + 5.2 > 6.1
4.3 + 6.1 > 5.2
5.2 + 6.1 > 4.3 <
7.17.2
436-439444-445
3, 5, 13-17 odd, 24, 26, 31, 39, 403-7 odd, 15-21 odd, 25
HW Problem
7.1 #26
Ans:
c2 = a2 + b2
52 = a2 + 32
25 = a2 + 916 = a2
aH H
4 = a
c2 = a2 + b2
x2 = 42 + 72
x2 = 16 + 49x2 = 65
65x
