Notes 6-2 Pythagorean Theorem Converse

Notes 6-2 Pythagorean Theorem Converse

Pythagorean Theorem Converse

§  Pythagorean Theorem – If a triangle is a right triangle with legs “a” and “b” and hypotenuse “c”, then a2 + b2 = c2.

§  Pythagorean Theorem Converse –

Given the following numbers, determine:

1)  if it is possible to form a triangle with the given sides, and

2)  if so, tell whether the triangle is a right triangle or not.

Ex 1: 3, 4, 5 Ex 2: 3, 4, 6

Ex 3: 5, 10, 16 Ex 4: 3, 3, 4

Right Triangle Obtuse Triangle Acute Triangle

§  Therefore:

o  If a2 + b2 > c2, then

o  If a2 + b2 < c2, then

Given the following numbers, determine:

1)  if it is possible to form a triangle with the given sides, and

2)  if so, tell whether the triangle is right, acute, or obtuse.

Ex 5: 3, 4, 5 Ex 6: 3, 4, 6

Ex 7: 5, 10, 16 Ex 8: 3, 3, 4