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3.4
Is It A Right Triangle?
Pg. 13Pythagorean Theorem Converse and Distance
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3.4 – Is It A Right Triangle?_______________Pythagorean Theorem Converse and Distance
In lesson 3.3, you learned how to use the Pythagorean Theorem. Today you are going to use this information to find the length between two points on a graph. You are also going to determine if the triangle is acute, right, or obtuse.
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3.24 – DISTANCEUse the Pythagorean theorem to find the following.
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A
B
7
3
d
49 + 9 = d2
58 = d2
l2 + l 2 =h2
58 =d
72 + 32 = d2
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b. A(-6, 2)and B(-2, -3)
A
B
5
4
d16 + 25 = d2
41 = d2
l2 + l 2 =h2
41 =d
42 + 52 = d2
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c. A(-1, 2)and B(3, 4)
A
B2
4
x
4 + 16 = d2
20 = d2
l2 + l 2 =h2
2 5 =d
22 + 42 = d2
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Distance Formula:
x2 – x1
y2 – y1
2 2 2x y d
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3.25 – DISTANCE FORMULAFind the distance between the two points. Simplify your square roots.
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a. A(2, 4)and B(8, 19)
2 2 2x y d 62 + 152 = d2
36 + 225 = d2
261 = d2
d = 3 29
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b. A(-2, 3)and B(-8, 6)
2 2 2x y d 62 + 32 = d2
36 + 9 = d2
45 = d2
d = 3 5
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c. A(-5, 2)and B(-2, -7)
2 2 2x y d 32 + 92 = d2
9 + 81 = d2
90 = d2
d = 3 10
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3.26 – WHAT'S THE PATTERN?Use the tools you have developed to find the lengths of the missing sides of the triangles below. If you know a shortcut, share it with your team. Look for any patterns in the triangles as you solve. Are any triangles similar and multiples of others? Keep answers in exact form.
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2 2 23 4x
5
2 2 26 8x
10
2 2 23000 4000x
5000
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2 2 213 5x
12
2 2 226 10x
24
2 2 2130 50x
120
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3.27 – PYTHAGOREAN TRIPLES
4
3
512
5
13
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3.28 – EXTRA PRACTICEFind the area of the shapes using Pythagorean triples to help find the missing sides.
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8
3
4
triangle rectangleA 1
2
A bh bh
1 4 3
2A 8 3
6A 24 230un
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81
2A bh
136 8
2A
2144A un
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5
530
30 20
20
A = 100un2
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Right TriangleAcute
TriangleObtuse Triangle
b
a
c
2 2 2c a b
b
a
c
2 2 2c a b
b
a
c
2 2 2c a b
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3.29 – TRIANGLE CLASSIFICATIONFor each set of numbers, determine if the triangle is acute, right, or obtuse. SHOW WORK!
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a. 8, 15, 17
2 2 217 8 15 289 64 225
289 289
ACUTE, RIGHT, or OBTUSE
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b. 3, 5, 7
2 2 27 3 5 49 9 25 49 34
ACUTE, RIGHT, or OBTUSE
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c. 8, 10, 12
2 2 212 8 10 144 64 100 144 164
ACUTE, RIGHT, or OBTUSE
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d.
ACUTE, RIGHT, or OBTUSE
22 289 5 8
89 25 64 89 89
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e.
22 28 5 3 7
64 25 63 64 88
ACUTE, RIGHT, or OBTUSE
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f.
22 212 2 10 9
144 40 81 144 121
ACUTE, RIGHT, or OBTUSE