Page 157 - Math Course 2 (Book 1)

The Pythagorean Theorem

MO. 5 - L4b

Using The Converse of the

Pythagorean Theorem Let’s Begin

Vocabulary A-Z

Let us learn some vocabulary Standardized Test Example

A building is 10 feet tall. A ladder is positioned
against the building so that the base of the ladder
is 3 feet from the building. About how long is the
Converse ladder in feet?

The Pythagorean Theorem is written in if-then form. A . 10.0 feet B. 12.4 feet
If you reverse the statements after if and then, you C. 10.4 feet D . 14.9 feet 10 ft
have formed the converse of the Pythagorean
Theorem.
3 ft
Read the Test Item
Pythagorean Theorem Make a drawing to illustrate the problem. The
2
2
If a triangle is a right triangle, then c = a + b 2 ladder, ground, and side of the house form a right
triangle.
Solve the Test Item
2
2
2
If c = a + b , then a triangle is a right triangle. Use the Pythagorean Theorem to f nd the length of
Converse the ladder.
Key Concept c = a + b 2 Pythagorean Theorem
2
2
2
2
Pythagorean Theorem c = 3 + 10 2 Replace a with 3 and b with 10.
2
c = 9 + 100 Evaluate 32 and 102.
Words If a triangle is a right triangle, then the
2
square of the length the hypotenuse is c = 109 Simplify.
equal to the sum of the squares of the
2
c = 109 Take the square root of each side.
lengths of the legs.
c = 10.4 Round to the nearest tenth.
2
2
Model Symbols c = a + b 2
a c Example 5 = 3 + 4 2
2
2
25 = 9 + 16 Answer The ladder is about 10.4 feet tall.
25 = 25
b

Identify a Right Triangle 78 = 48 + 60 Replace c with 78, a with 48,
2
2
2
and b with 60.
Examples 6084 = 2304 + 3600 Evaluate 782, 482, and 602.
6084 ≠ 5904 Simplify
The measures of three sides of a triangle are given.
Determine whether the triangle is a right triangle. The triangle is not a right triangle.
48 ft, 60 ft, 78 ft

2
2
c = a + b 2 Pythagorean Theorem Answer NO
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