Warmup

1

• Warmup
• Find the area of a square whose sides are 10
  units long.
• The square of what number is 2704?
• Evaluate each expression.
• a. 82 32
• b. 122 52

2

• Notes Section 3.6 The Pythagorean Theorem
• Objective Write the converse of a conditional
  statement.
• Terms to Know
• Leg (p. 141)
• Hypotenuse (p. 141)
• Squares and Square Roots
• You will use squares and positive square roots
  when finding the lengths of the sides of a right
  triangle.
• The Pythagorean Theorem
• You can use the Pythagorean Theorem to find an
  unknown length of a right triangle whenever the
  other two side lengths are known. In a right
  triangle, the sum of the squares of the lengths
  of the legs is equal to the square of the length
  of the hypotenuse.

3

• Example 1
• The legs of a right triangle are a and b units
  long. The hypotenuse is c units long. Find the
  unknown length for each right triangle, to the
  nearest hundredth.
• a. a4, b9
• b. b12, c13
• Converse of the Pythagorean Theorem
• The converse of the Pythagorean theorem is true.
  You can use it to determine if a triangle with
  given side lengths is a right triangle. If a, b
  and c are the lengths of the sides of a triangle
  and a2 b2 c2, then the triangle is a right
  triangle.
• Example 2
• Can the given numbers be the lengths of the
  sides of a right triangle?
• a. 7, 8, 11
• b. 6, 8, 10

4

• Example 3
• Anguel is remodeling an old house that he
  recently bought. He has decided to put new tiles
  on the floor of the bathroom. Each tile is
  square and therefore has corners that are 90º.
  Anguel wants to check that the angle of the floor
  corner is 90º, using the measurements shown.