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# Pythagorean Theorem and Its Converse

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on 7 January 2014

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#### Transcript of Pythagorean Theorem and Its Converse

Pythagorean Theorem and Its Converse
Pythagorean Triple
set of lengths of the sides of a triangle satisfying the converse of the Pythagorean Theorem
a = 5
b = 12
c = 13
CONVERSE OF
PYTHAGOREAN
THEOREM
IF THE SQUARE OF THE LENGTH OF ONE SIDE OF A TRIANGLE EQUALS THE SUM OF THE SQUARES OF THE LENGTHS OF THE OTHER TWO SIDES, THEN THE TRIANGLE IS A RIGHT TRIANGLE.
a = 4
b = sqrt 67
c = 9
a = 8
b = 15
c = 19
a = 10
b = 11
c = 14
Pythagorean Theorem
- In any right triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the lengths of the legs (a and b). In symbols .
a = 3
b = 4
c = 5
a = 27
b = 36
c = 45
a = 6
b = 8
c = 10
a = 5
b = 12
c = 13
a = 9
b = 12
c = 15
Am I a Right Triangle?
a = 18
b = 24
c = 30
Find the unknown side. Simplify answers that are radicals.
Problem Solving
1. A wire is stretched from the top of an 8 ft pole to a bracket 5 ft from the base of the pole. How long is the wire?
2. A helicopter rose vertically 300 m then flew west 400 m. How far was the helicopter from its starting point?
3. A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along two sides of it?
4. Anna has let out 50 m of kite string when she observes that her kite is directly above Emily. If Anna is 35 m from Emily, how high is the kite?
5. A 50-ft cable is stretched from the top of an antenna to an anchor point on the ground 15 ft from the base of the antenna. How tall is the antenna?
6. Two trains left Metropolis at the same time. One traveled south at 50 mph. The other traveled east at 40 mph. How far apart were the trains at the end of 3 hours?
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