The Rule of Pythagoras

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The Rule of Pythagoras

• Pythagorean Theorem

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Quick Review
Hypotenuse
c

• What is a right triangle?
• Sides of a triangle are defined by their
  position with respect to the _________ ________.
• What is the hypotenuse?
• What are the other two sides called?
• The hypotenuse is always the ___________ side.

The side always opposite the right angle always
labeled c
Legs always labeled a and b
longest
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Pythagorean Theorem
The rule of Pythagoras is IF A triangle is a
right triangle THEN A triangle has legs a,b, and
c such that a2b2c2
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Proof of Pythagorean Theorem
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Practice Together

• If you know the triangle is right or contains a
  right angles then you can find the sides. Find x.

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You Do
3/4 cm
1/2 cm
?10 cm
x cm
x cm
x cm
4 cm
3 cm
x cm

• Find the value of x

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Where else is the Pythagorean Theorem useful???

• Special Geometrical Figures

Equilateral Triangle
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Steps to Solving a Problem with Geometrical
Figures

1. Draw a neat, clear diagram of the situation
2. Mark on diagram known length and right angles
3. Use a symbol, such as x, to represent unknown
   length
4. Write down Pythagorean Theorem for the given
   information
5. Solve the equation
6. Write your answer in sentence form (where
   necessary)

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Practice

• A rhombus has diagonals of length 6 cm and 8 cm.
  Find the length of its sides.

• Solve

x cm
a2b2c2 6282x2 3664x2 100x2 v100vx2 10x
6 cm
8 cm
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You Do

• An isosceles triangular garden bed has equal
  sides 12 m long and the third side is 10 m. Find
• The altitude of the triangle
• The area of the triangle

• Solve

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You Do

• A rectangle has a diagonal of length 15 inches.
  The longer side of the rectangle is twice as long
  as the shorter side. What is the area of the
  rectangle?

• Solve

2x
x
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Write your own!

• Write your own problem in which you must use the
  Pythagorean Theorem to find an unknown
  measurement in a geometric figure.
• Exchange problems with your partner and solve.