Pre-Algebra HOMEWORK

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Pre-Algebra HOMEWORK

• Page 292
• 8-15

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Our learning goal is to be able to solve for
perimeter, area and volume.

• Learning Goal Assignments
• Perimeter and Area of Rectangles and
  Parallelograms
• Perimeter and Area of Triangles and Trapezoids
• The Pythagorean Theorem
• Circles
• Drawing Three-Dimensional figures
• Volume of Prisms and Cylinders
• Volume of Pyramids and Cones
• Surface Area of Prisms and Cylinders
• Surface Area of Pyramids and Cones
• Spheres

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6-3
The Pythagorean Theorem
Learning Goal Assignment Learn to use the
Pythagorean Theorem and its converse to solve
problems.
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6-3
The Pythagorean Theorem
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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Warm Up Graph the figures with the given
verticals and find the area. 1. (1, 1), (1,
3), (6, 1) 2. (2, 1), (8, 1), (6, 3) 3. (3,
2), (15, 2), (14, 6), (4, 6)
14 units2
12 units2
88 units2
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Problem of the Day A side of a square A is 5
times the length of square B. How many times as
great is the area of square A than the area of
square B?
25
7
6-3
The Pythagorean Theorem
Learning Goal Assignment Learn to use the
Pythagorean Theorem and its converse to solve
problems.
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Vocabulary
Pythagorean Theorem leg hypotenuse
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(No Transcript)
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Additional Example 1A Find the the Length of a
Hypotenuse
Find the length of the hypotenuse.
c
A.
4
5
Pythagorean Theorem
a2 b2 c2
Substitute for a and b.
42 52 c2
16 25 c2
Simplify powers.
41 c2
6.40 ? c
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Try This Example 1A
Find the length of the hypotenuse.
c
A.
5
7
Pythagorean Theorem
a2 b2 c2
Substitute for a and b.
52 72 c2
Simplify powers.
25 49 c2
8.60 ? c
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Additional Example 1B Find the the Length of a
Hypotenuse
Find the length of the hypotenuse.
triangle with coordinates
B.
(1, 2), (1, 7), and (13, 2)
Pythagorean Theorem
a2 b2 c2
Substitute for a and b.
92 122 c2
81 141 c2
Simplify powers.
15 c
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Try This Example 1B
Find the length of the hypotenuse.
B. triangle with coordinates (2, 2), (2, 4),
and (3, 2)
(2, 4)
The points form a right triangle.
a2 b2 c2
Pythagorean Theorem
62 52 c2
Substitute for a and b.
36 25 c2
Simplify powers.
(2, 2)
(3, 2)
7.81 ? c
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Additional Example 2 Finding the Length of a Leg
in a Right Triangle
Solve for the unknown side in the right triangle.
Pythagorean Theorem
a2 b2 c2
25
Substitute for a and c.
72 b2 252
b
Simplify powers.
49 b2 625
49 49
b2 576
7
b 24
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Try This Example 2
Solve for the unknown side in the right triangle.
a2 b2 c2
Pythagorean Theorem
12
b
Substitute for a and c.
42 b2 122
Simplify powers.
16 b2 144
16 16
4
b2 128
b ? 11.31
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Additional Example 3 Using the Pythagorean
Theorem to Find Area
Use the Pythagorean Theorem to find the height of
the triangle. Then use the height to find the
area of the triangle.
a2 b2 c2
Pythagorean Theorem
Substitute for b and c.
a2 42 62
a2 16 36
6
6
a
a2 20
4
4
Find the square root of both sides.
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Try This Example 3
Use the Pythagorean Theorem to find the height of
the triangle. Then use the height to find the
area of the triangle.
a2 b2 c2
Pythagorean Theorem
a2 22 52
Substitute for b and c.
5
5
a2 4 25
a
a2 21
2
2
Find the square root of both sides.
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Lesson Quiz
Use the figure for Problems 1-3.
1. Find the height of the triangle.
8m
2. Find the length of side c to the nearest
meter.
c
10 m
h
12m
3. Find the area of the largest triangle.
6 m
9 m
60m2
4. One leg of a right triangle is 48 units long,
and the hypotenuse is 50 units long. How long is
the other leg?
14 units