The student will be able to:

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The student will be able to
Validate and apply Pythagorean Theorem to find
distances in real world situations or between
points in the coordinate plane.
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Lets Review the Pythagorean Theorem!
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What is a right triangle?
hypotenuse
leg
right angle
leg

• It is a triangle which has an angle that is 90
  degrees.
• The two sides that make up the right angle are
  called legs.
• The side opposite the right angle is the
  hypotenuse.

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The Pythagorean Theorem

• In a right triangle, if a and b are the measures
  of the legs and c is the hypotenuse, then
• a2 b2 c2.
• Note The hypotenuse, c, is always the longest
  side.

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1. Find the length of the hypotenuse

• 122 162 c2
• 144 256 c2
• 400 c2
• Take the square root
• of both sides.

12 in
16 in
The hypotenuse is 20 inches long.
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2. Find the length of the hypotenuse

• 52 72 c2
• 25 49 c2
• 74 c2
• Take the square root of both sides.

5 cm
7 cm
The hypotenuse is about 8.6 cm long.
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3. Find the length of the hypotenuse given that
the legs of a right triangle are 6 ft and 12 ft.

1. 180 ft.
2. 324 ft.
3. 13.42 ft.
4. 18 ft.

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4. Find the length of the missing leg.

• 42 b2 102
• 16 b2 100
• -16 -16
• b2 84

The leg is about 9.2 cm long.
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5. Find the length of the missing leg.

• a2 122 132
• a2 144 169
• -144 -144
• a2 25

The leg is 5 inches long.
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6. Find the length of the missing side of a
right triangle if one leg is 4 ft and the
hypotenuse is 8 ft.

1. 24 ft.
2. 4 ft.
3. 6.9 ft.
4. 8.9 ft.

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Application of Pythagorean Theorem
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Application of Pythagorean Theorem

• A baseball diamond is a square with 90-foot
  sides. What is the approximate distance the
  catcher must throw from home to second base?

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The Distance Formula
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Deriving the Distance Formula
The Distance from Point A to Point B would be
equal to the length of the hypotenuse of triangle
ABC.
C
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Find the Distance Between

• Points A and B
• Points B and C
• Points A and C

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• Each square on the grid represents one square
  mile.
• One route from the high school to the middle
  school requires traveling northeast on Lookout
  Road.
• A different route from the high school to the
  middle school requires traveling east on Broadway
  then north on Main Street.

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