pythagorean theorem and its converse
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Pythagorean Theorem and its converse. Section 8-1. 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. a 2 + b 2 = c 2. c. Hypotenuse. a. Leg. b. Leg. Example 1. - PowerPoint PPT PresentationTRANSCRIPT
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Pythagorean Theorem and its converse
Section 8-1
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Pythagorean TheoremIn a right triangle the sum of the squares of the
measures of the legs equals the square of the measure of the hypotenuse.
a2 + b2 = c2
ac
b
Leg
Leg
Hypotenuse
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Lesson 7-2: The Pythagorean Theorem 8
Example 1
A
B
C
In the following figure if A = 8 and B = 6, Find C.
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Lesson 7-2: The Pythagorean Theorem 9
Pythagorean Theorem : Examples 2 and 32. A=8, B= 15, Find C
3. A=7, B= 24, Find C
A
B
C
C = 17
C = 25
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Solve for x
x 3
5
4.
5. x 4
6
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Word problems ex. 6The foot of a ladder is 6 feet from a wall. If
the top of the ladder rests 8 feet up a wall, how long is the ladder?
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Example 7
Randy made a ramp for his dog to get into his truck. The ramp is 6 ft long and the bed of the truck is 3ft above the ground. Approximately how far from the back of the truck does the ramp touch the ground?
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Example 8Donna’s TV screen is 20 inches long. If the
diagonal measures 25 inches, what is the width of the tv screen?
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Example 9Town A is 9 miles from town B, and 12 miles
from town C. A road connects towns B and C directly. Find the length of this road. Angle B is the right angle.
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Converse of the Pythagorean theoremIf the sum of the square 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.
If a2 + b2 = c2, then ∆ABC is a right triangle.
a
C
B
A b
c
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Tell whether it is a right triangle:10.
9
15
343 11.
14 2
2 26
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