Prentice Hall Lesson 11.2EQ: What is the Pythagorean Theorem?

BOP:

Solution to BOP:

Homework Questions?

Prentice Hall Lesson 11.2What is the Pythagorean Theorem?

Toolbox:• In a right triangle, each of the sides forming the right angle is a leg. The side opposite the right angle is the hypotenuse, which is also the longest side.• The Pythagorean Theorem: In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

a² + b² = c² a c

b

• An if-then statement is called a conditional. The part following the “if” is the hypothesis, and the part following the “then” is the conclusion.

• The converse of a conditional switches the hypothesis and the conclusion, which may or may not give a true statement.

• The Converse of the Pythagorean Theorem: If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle with hypotenuse of length c. You can use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

What is the length of the hypotenuse of this triangle?

ALGEBRA 1 LESSON 11-2ALGEBRA 1 LESSON 11-2

a2 + b2 = c2 Use the Pythagorean Theorem.

82 + 152 = c2 Substitute 8 for a and 15 for b.

64 + 225 = c2 Simplify.

289 = c2 Find the principal square root of each side.

17 = c Simplify.

The length of the hypotenuse is 17 m.

11-2

A toy fire truck is near a toy building on a table such that the base of the

ladder is 13 cm from the building. The ladder is extended 28 cm to the

building. How high above the table is the top of the ladder?

ALGEBRA 1 LESSON 11-2ALGEBRA 1 LESSON 11-2

Define: Let b = height (in cm) of the ladder from a point 9 cm above the table.

Relate: The triangle formed is a right triangle. Use the Pythagorean Theorem.

11-2

ALGEBRA 1 LESSON 11-2ALGEBRA 1 LESSON 11-2

Write: a2 + b2 = c2

132 + b2 = 282 Substitute.169 + b2 = 784 Simplify.

b2 = 615 Subtract 169 from each side.

b2 = 615 Find the principal square root of each side.

b 24.8 Use a calculator and round to the nearest tenth.

(continued)

The height to the top of the ladder is 9 cm higher than 24.8 cm, so it is about 33.8 cm from the table.

11-2

Determine whether the given lengths are sides of a right triangle.

ALGEBRA 1 LESSON 11-2ALGEBRA 1 LESSON 11-2

a. 5 in., 5 in., and 7 in.

This triangle is not a right triangle.

b. 10 cm, 24 cm, and 26 cm

This triangle is a right triangle.

100 + 576 676 Simplify. 676 = 676

102 + 242 262 Determine whether a2 + b2 = c2, where c is the longest side.

52 + 52 72 Determine whether a2 + b2 = c2, where c is the longest side.

25 + 25 49 Simplify. 50 = 49/

11-2

ALGEBRA 1 LESSON 11-2ALGEBRA 1 LESSON 11-2

If two forces pull at right angles to each other, the

resultant force is represented as the diagonal of a rectangle,

as shown in the diagram. The diagonal forms a right triangle

with two of the perpendicular sides of the rectangle.

For a 50–lb force and a 120–lb force, the resultant force is 130 lb. Are the forces pulling at right angles to each other?

16,900 = 16,900

The forces of 50 lb and 120 lb are pulling at right angles to each other.

502 + 1202 1302 Determine whether a2 + b2 = c2 where c is the greatest force.

2500 + 14,400 16,900

11-2

1.Find the missing length 2. Find the missing lengthto the nearest tenth. to the nearest tenth.

3.A triangle has sides of lengths12 in., 14 in., and 16 in. Is thetriangle a right triangle?

4.A triangular flag is attached to a post. The bottom of the flag is 48 in. above the ground. How far from the ground is the top of the flag?

16.6 5.7

no

57 in.

When you are finished, read pg. 598- 599 and complete problems #1 – 5, 7 - 9. Turn in all 12 problems.

Summary:Don’t forget to write your minimum three sentence summary answering today’s essential question on your summary paper!