8.1 handout pythagorean theorem and its converse.notebook Pythagorean... · 8.1 handout pythagorean...
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8.1 handout pythagorean theorem and its converse.notebook
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GeometryCh. 8 Handout 8.1
The Pythagorean Theorem and its Converse
8.1 handout pythagorean theorem and its converse.notebook
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Pythagorean Theorem1.2.
Works only on right triangles.
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a(leg)
b(leg)
c(hypotenuse)
8.1 handout pythagorean theorem and its converse.notebook
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A Pythagorean Triple is a set of nonzero whole numbers a, b, and c that satisfy the equation Here are some common Pythagorean triples:
3, 4, 5 5, 12, 138, 15, 17 7, 24, 25
If you multiply each number in a Pythagorean triple by the same whole number, the three numbers that results also form a Pythagorean triple.
8.1 handout pythagorean theorem and its converse.notebook
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1. Find the length of the hypotenuse of
A
B
C
12
5
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2. A right triangle has a hypotenuse of length 25 and a leg of length 10. Find the length of the otherleg.
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3. Find the value of b. Leave you answer in simplest radical form.a.
12 8
b
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3. Find the value of b. Leave you answer in simplest radical form.
b.8
14
x
8.1 handout pythagorean theorem and its converse.notebook
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3. Find the value of b. Leave you answer in simplest radical form.
c.9
12
x
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4. The hypotenuse of a right triangle has length 12. One leg has length 6. Find the length of the other leg. Leave your answer in simplest radical form.
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5. A baseball diamond is a square with 90ft sides. Home plate and second base are at opposite vertices of the square. About how far is home plate from second base?
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Theorem 82: Converse of Pythagorean TheoremIf the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
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Theorem 83If 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.
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Theorem 84If 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.
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is a right triangleis an obtuse triangleis an acute triangle
a
b
c
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Classify each triangle as Acute, Obtuse, or Right Triangle.
4 m
6 m7 m
26 m 24 m
10 m
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Classify each triangle as Acute, Obtuse, or Right Triangle.
10, 15, and 201) 16, 48, and 502)
3) 7, 8, and 9
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6. The town of Elena is 24 mi north and 8 mi west of Holberg. A train runs on a straight track between the two towns. How many miles does it cover? Round your answer to the nearest whole number.
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What is the distance from A to B? (to the nearest mile)
210 m
South Dakota
What is the distance from A to B? (to the nearest mile)
North Dakota
A
B340 m
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12 ft
43 ft
How high off the ground is Ollie the owl?
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Assignment:
Day 1: pgs 420421 115 odds, 17, 27, 29
Day 2: pgs 420421 216 evens, 1826 all, 28, 5964