Chapter 7.1

1
Chapter 7.1 7.2 Notes The Pythagorean Theorem
and its Converse

• Goal To use the Pythagorean Theorem and its
  Converse.

2

• Right Triangles
• In a right triangle, the side opposite the right
  angle is the longest side, called the hypotenuse.
  The other two sides are the legs of a right
  triangle.
• Theorem 7.1 Pythagorean Theorem
• 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.
• a2 b2 c2

3

• Find the value of x. Leave your answer in
  simplest radical form.
• Ex.1 Ex.2
• Ex.3 A 16-foot ladder rests against the side of
  the house, and the base of the ladder is 4 feet
  away. Approximately how high above the ground is
  the top of the ladder?

4

• When the lengths of the sides of a right triangle
  are integers, the integers form a Pythagorean
  Triple.
• Common Pythagorean Triples and Some of Their
  Multiples

3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
3x, 4x, 5x 5x, 12x, 13x 8x, 15x, 17x 7x, 24x, 25x
6, 8, 10 10, 24, 26 16, 30, 34 14, 48, 50
9, 12, 15 15, 36, 39 24, 45, 51 21, 72, 75
30, 40, 50 50, 120, 130 80, 150, 170 70, 240, 250
5

• Ex.4 Find the area of the isosceles triangle
  with side lengths 10 meters, 13 meters, and 13
  meters.
• Find the value of x. Leave your answer in
  simplified radical form.
• Ex.5 Ex.6

6

• Theorem 7.2 Converse of the Pythagorean Theorem
• If the square of the length of the longest side
  of a triangle is equal to the sum of the squares
  of the lengths of the other two sides, then the
  triangle is a right triangle.
• If c2 a2 b2, then ?ABC is a right triangle.

7

• Tell whether a triangle with the given side
  lengths is a right triangle.
• Ex.7 5, 6, Ex.8 10,
  11, 14
• Ex.9
• 8
• 4

8

• The Converse of the Pythagorean Theorem is used
  to determine if a triangle is a right triangle,
  acute triangle, or obtuse triangle.
• If c2 a2 b2, then the triangle is a right
  triangle.
• If c2 gt a2 b2, then the triangle is an obtuse
  triangle.
• If c2 lt a2 b2, then the triangle is an acute
  triangle.

9

• Determine if the side lengths form a triangle. If
  so, classify the triangle as acute, right, or
  obtuse.
• Ex.10 15, 20, and 36 Ex.11 6, 11, and 14
• Ex.12 8, 10, and 12 Ex.13 4.3, 5.2, and
  6.1