8.1 The Pythagorean Theorem and Its Converse

1
8.1 The Pythagorean Theorem and Its Converse
2
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

3
Pythagorean triple

• Pythagorean triple a set of nonzero whole
  numbers a, b, and c that satisfy the equation
• 3,4,5
• 5,12,13
• 8,15,17
• 7,24,25

4
Converse of the Pythagorean Theorem

• What if a²b² ? c²? Then what kind of triangle
  is formed?
•  
• Acute Triangle if c² lt a² b²
• Obtuse Triangle if c² gt a² b²
• These two facts need to be memorized for the
  test.
• Dont forget if c² a² b² then the
  triangle is a Right Triangle.

5
Practice 1

• The hyp of a right triangle is 12 m and the leg
  is 5 m. Find the length of the other leg.

6
Practice 2

• The legs of a right triangle are 10 ft. and 8 ft.
  Find the length of the hypotenuse.

7
Practice 3

• The hypotenuse of an isosceles right triangle is
  18 mi. long. Find the lengths of both legs

8
Simplify 1

• v12

9
Simplify 2

• v150

10
Homework/Classwork

• Pgs 420-421 2-28e, 36-46e