Page 170 - Math Course 2 (Book 1)

The Pythagorean Theorem and Its Converse

Your Turn! MO. 5 - L7b

Find the Length of the Hypotenuse Using the Converse of the
Pythagorean Theorem
LONGITUDE AND LATITUDE
Carson City, Nevada, is located at about 120
degrees longitude and 39 degrees latitude. NASA Pythagorean triple
Dryden is located about 117 degrees longitude and
34 degrees latitude. Use the lines of longitude and A group of three whole numbers that satisfy the
latitude to f nd the degree distance to the nearest Pythagorean Theorem is called a Pythagorean triple.
tenth of a degree if you were to travel directly from
NASA Dryden to Carson City. c 17 13
a 8 5
A. about 5.8 degrees
B. about 8.5 degrees b 15 12
2
2
C. about 10 degrees a = b + c 2
D. about 12.5 degrees
Converse
Answer
If you exchange the hypothesis and conclusion of an
if-then statement, the result is the converse of the
statement.

If it is raining If a triangle is a right triangle
2
2
then the grass is wet. then a + b = c 2
Converse: Converse:
2
2
If the grass is wet. If a + b = c 2
then it is raining. then the triangle is a right
triangle.
Find the Length of a Leg
Find x. Round your answer to the nearest tenth.

A. 17 A THEOREM 5.2
B. 12.7 15 cm
C. 11.5 8 cm
D. 13.2 Converse of the
C x cm B Pythagorean Theorem
Answer
If the sum of the squares 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.

2
2
2
Symbols a + b = c , then ΔABC is a right triangle
B
c
a
A b C

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