geometry section 9.3 pythagorean theorem converse
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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
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