Page 161 - Math Course 2 (Book 1)

Radical Expressions: Pythagorean Theorem

Find the Length of a Side
MO. 5 - L5b

Example Determining a Right Triangle

Find the length of the missing side.
If necessary, round to the nearest b 16
hundredth. Vocabulary A-Z
9 Let us learn some vocabulary
2
2
c = a + b 2 Pythagorean Theorem
2
2
16 = 9 + b 2 a = 9 and c = 16
256 = 81 + b 2 Evaluate squares. Pythagorean triple

175 = b 2 Subtract 81 from each side. A group of three whole numbers that satisfy the
Pythagorean Theorem is called a Pythagorean triple.
+ 175 = b Use a calculator to evaluate
175. c 17 13
a 8 5
13.23 = b Use the positive value. b 15 12
2
2
a = b + c 2
Answer about 13.23 units

Converse
Your Turn! If you exchange the hypothesis and conclusion of an
if-then statement, the result is the converse of the
Find the Length of the Hypotenuse statement.

Find the length of the hypotenuse of a right triangle If it is raining If a triangle is a right triangle
if a = 25 and b = 60. then the grass is wet. then a + b = c 2
2
2
A. 45 units Converse: Converse:
B. 85 units If the grass is wet. If a + b = c 2
2
2
C. 65 units
D. 925 units then it is raining. then the triangle is a right
triangle.
Answer

Find the Length of a Side Key Concept

Find the length of the missing side.
Converse of the
a 17
A. about 12 units Pythagorean Theorem
B. about 22 units
C. about 16.25 units 5 If a and b are measures of the shorter sides of a
D. about 5 units triangle, c is the measure of the longest side, and
2
2
2
c = a + b , then the triangle is a right triangle.
2
2
2
Answer If c ≠ a + b , then the triangle is not a right
triangle.

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