Section 8'1 and the Pythagorean Theorem

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Section 8.1 and the Pythagorean Theorem

• Solving Quadratic Equations by Completing the
  Square
• Note Please substitute 11 for 13 in the
  homework.

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Solving Quadratic Equations using the Square Root
Property

• Suppose we had the quadratic equation
• Ie, tell me all the numbers that, when squared,
  give me 4.
• How many are there?
• What are the solutions?
• Note This is different from simply evaluating
  the square root,
• For this, give only the principal root
• When solving an equation, give both positive and
  negative roots. (ie, two solutions!)

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The Square Root Property

• When you have a quadratic equation of the form
• then you can solve by taking the square root
  of both sides.
• Ie The Square Root Property
• If then

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Examples
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Now, on to the Pythagorean Theorem!

• Supplement is on LS Math 0099 webpage. It has
  additional problems that you need to work.
• Important note Dont try to use the Square Root
  Property on all of these! Some need to be
  factored.

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The Pythagorean Theorem!

• Right triangles are special triangles, ones that
  contain a right angle.
• A right angle is a 90 degree angle.
• The longest side, the hypotenuse, is the side
  opposite the right angle.
• The other 2 sides are called the legs.
• The Pythagorean Theorem states
• In a right triangle, the square of the hypotenuse
  length is equal to the sum of the squares of the
  lengths of the legs. In other words

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Example

• In a right triangle, the hypotenuse has length
  12, and a leg of length 8. Find the length of the
  other leg.

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Example (supplement 2)

• A lot is in the shape of a right triangle. The
  longer leg of the triangle is 20 yards longer
  than twice the length of the shorter leg. The
  hypotenuse is 30 yards longer than twice the
  length of the shorter leg. What are the lengths
  of the three sides?