Learn the Pythagorean Theorem and its converse

1

• Learn the Pythagorean Theorem and its converse
• Learn about special right triangles that follow
  from the Pythagorean Theorem
• Use the Pythagorean Theorem to find the distance
  between two points on a coordinate plane
• Use the Pythagorean Theorem to solve word
  problems

2
The Pythagorean Theorem

• The Greek mathematician Pythagoras, who lived
  about 2500 years ago, discovered a relationship
  between the lengths of the sides of a right
  triangle
• The hypotenuse of a right triangle is the side
  opposite the right angle
• The legs of a right triangle are the sides that
  meet at the right angle
• Since the right angle is the largest angle in the
  right triangle, the hypotenuse is the longest
  side
• C-82 The Pythagorean Theorem
• In a right triangle, the sum of the squares of
  the lengths of the legs equals the square of the
  length of the hypotenuse.
• If a and b are the lengths of the legs, and c is
  the length of the hypotenuse, then a2 b2 c2

hypotenuse
legs
3
The Pythagorean Theorem

• Given two sides of a right triangle, you can use
  the Pythagorean Theorem to find the length of the
  third side
• The two legs a and b can be used in any order
• The hypotenuse is always the c in the formula
• Proving the Pythagorean Theorem
• There are over 200 proofs of the Pythagorean
  Theorem, written by people ranging from
  Pythagoras and Euclid to Leonardo DaVinci and
  even President James Garfield
• The figure at right contains four congruent right
  triangles with sides a, b, and c, arranged around
  a square that has the hypotenuse as its sides
• The area of the large square is (a b)2, or a2
  2ab b2
• The area of each triangle is ½ ab, so the area of
  all four is 2ab
• Subtracting the area of the triangles from area
  of the large square gives a2 2ab b2 2ab, or
  a2 b2
• This equals the area of the blue square, so a2
  b2 c2

hypotenuse
legs