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Prentice Hall Lesson 11.2
EQ: What is the Pythagorean Theorem?
BOP:
Solution to BOP:
Homework Questions?
Prentice Hall Lesson 11.2
What 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.
a
c
a² + b² = c²
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.
ALGEBRA 1 LESSON 11-2
What is the length of the hypotenuse of this triangle?
a2 + b2 = c2
Use the Pythagorean Theorem.
82 + 152 = c2
Substitute 8 for a and 15 for b.
64 + 225 = c2
289 =
17 = c
c2
Simplify.
Find the principal square root of each side.
Simplify.
The length of the hypotenuse is 17 m.
11-2
ALGEBRA 1 LESSON 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?
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 11-2
(continued)
Write:
a2 + b2 = c2
132 + b2 = 282
169 + b2 = 784
Substitute.
Simplify.
b2 = 615
Subtract 169 from each side.
b2 =
Find the principal square root of each side.
b
615
24.8
Use a calculator and round to the
nearest tenth.
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
ALGEBRA 1 LESSON 11-2
Determine whether the given lengths are sides of a right triangle.
a. 5 in., 5 in., and 7 in.
52 + 52
72
25 + 25 49
50 =/ 49
Determine whether a2 + b2 = c2,
where c is the longest side.
Simplify.
This triangle is not a right triangle.
b. 10 cm, 24 cm, and 26 cm
102 + 242 262
Determine whether a2 + b2 = c2,
where c is the longest side.
100 + 576 676
Simplify.
676 = 676
This triangle is a right triangle.
11-2
ALGEBRA 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?
502 + 1202
2500 + 14,400
1302
Determine whether a2 + b2 = c2
where c is the greatest force.
16,900
16,900 = 16,900
The forces of 50 lb and 120 lb are pulling at right angles to each other.
11-2
1. Find the missing length
to the nearest tenth.
2. Find the missing length
to the nearest tenth.
16.6
5.7
3. A triangle has sides of lengths
12 in., 14 in., and 16 in. Is the
triangle a right triangle? no
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?
57 in.
When you are finished, read pg. 598- 599 and
complete problems #1 – 5, 7 - 9. Turn in all 12 problems.
Summary:
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