5-Minute Check on Lesson 7-1

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Transparency 7-2
5-Minute Check on Lesson 7-1

• Find the geometric mean between each pair of
  numbers. State exact answers and answers to the
  nearest tenth.
• 9 and 13
  2. 2v5 and 5v5
• 3. Find the altitude
  4. Find x, y, and z
• 5.
  Which of the following is the best estimate of x?

v50 7.1
v117 10.8
x 8, y v80 8.9 z v320 17.9
z
y
x
8
3
4
v24 4.9
20
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Standardized Test Practice
x
5
12
A
C
B
D
2
10
11
12
C
Click the mouse button or press the Space Bar to
display the answers.
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Lesson 7-2

• Pythagorean Theorem and its Converse

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Objectives

• Use the Pythagorean Theorem
• If a right triangle, then c² a² b²
• Use the converse of the Pythagorean Theorem
• If c² a² b², then a right triangle

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Vocabulary

• None new

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Pythagorean Theorem
Pythagorean Theorem a2 b2 c2 Sum of the
squares of the legs is equalto the square of the
hypotenuse
Converse of the Pythagorean Theorem If the sum
of the squares of the measures of two sides of a
triangle equals the square of the measure of the
longest side, then the triangle is a right
triangle Remember from our first computer quiz
In an acute triangle, c2 lt a2 b2. In an
obtuse triangle, c2 gt a2 b2.
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Example 1
Find d.
Pythagorean Theorem
Simplify.
Subtract 9 from each side.
Take the square root of each side.
Use a calculator.
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Example 2
Find x.
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Pythagorean Triples

• For three numbers to be a Pythagorean triple they
  must satisfy both of the following conditions
• They must satisfy c2 a2 b2 where c is the
  largest number
• All three must be whole numbers (integers)
• Common Pythagorean Triples
• 3, 4, 5 5, 12, 13 8,
  15, 17
• 6, 8, 10
• 9, 12, 15 7, 24, 25
• 12, 16, 20
  9, 40, 41
• 15, 20, 25 10, 24, 26 16, 30, 34

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Example 3
Determine whether 9, 12, and 15 are the sides of
a right triangle. Then state whether they form a
Pythagorean triple.
Since the measure of the longest side is 15, 15
must be c. Let a and b be 9 and 12.
Pythagorean Theorem
Simplify.
Add.
Answer These segments form the sides of a right
triangle since they satisfy the Pythagorean
Theorem. The measures are whole numbers and form
a Pythagorean triple.
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Example 4
Determine whether 21, 42, and 54 are the sides of
a right triangle. Then state whether they form a
Pythagorean triple.
Pythagorean Theorem
Simplify.
Add.
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Example 5
Pythagorean Theorem
Simplify.
Add.
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Example 6
Answer The segments form the sides of a right
triangle and the measures form a Pythagorean
triple.
Answer The segments do not form the sides of a
right triangle, and the measures do not form a
Pythagorean triple.
Answer The segments form the sides of a right
triangle, but the measures do not form a
Pythagorean triple.
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Summary Homework

• Summary
• The Pythagorean Theorem can be used to find the
  measures of the sides of a right triangle
• If the measures of the sides of a triangle form a
  Pythagorean triple, then the triangle is a right
  triangle
• Homework
• pg 354, 17-19, 22-25, 30-35