Geometry Section 9.3

Pythagorean Theorem Converse

The converse of the Pythagorean Theorem is also true.

Pythagorean Theorem Converse

If the square of the largest side of a triangle equals the sum of the squares of the other two sides,

then the triangle is a right triangle.

ngle.right tria a is ABC then ,c If 222 ba

If a triangle is not a right triangle, then it must be either acute or

obtuse.

triangle.obtusean is ABC then ,c If 222 ba

triangle.acutean is ABC then ,c If 222 ba

NOTE: In all three of these statements, c must be the longest

side in the triangle!!!!

Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.

exist.cannot triangle then thesides, other two theof sumsidelongest If

53 64

27 8 222

obtuse

8.94 11.18 47.4

100 125

80 20 125

5452 55222

obtuse

Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.

07.7

61 50

65 25 222

acuteexistnot Does

1164

73

73

382

222

AC

AC

AC

_____73 AC 11

obtuse. is B that so AC of

lengths possible all expresses that inequality compound a Write