Converse of the Pythagorean Theorem 9.3 c = 10 c = 5 356 2 89 c 160 4 10 c 196 14 b
Converse of the Pythagorean Theorem 9.3 c = 10 c = 5.
Dec 26, 2015
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Converse of the Pythagorean Theorem9.3
c = 10 c = 5
356 2 89c 160 4 10c
196 14b
Converse of the Pythagorean Theorem9.3
Chapter 9Right Triangles and Trigonometry
Section 9.3
Converse of the Pythagorean Theorem
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE
Converse of the Pythagorean Theorem9.3
THEOREM
A
BC
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM 9.5 Converse of the Pythagorean Theorem
c 2 = a
2 + b 2
b
ac
In a triangle, if c2 = a2 + b2, then the triangle is a right triangle
ABC is a right Triangle
Converse of the Pythagorean Theorem9.3
THEOREM
AB
C
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM 9.6
c 2 < a
2 + b 2
In a triangle, if c2 < a2 + b2, then the triangle is acute
ABC is acuteba
c
Converse of the Pythagorean Theorem9.3
THEOREM
AC
B
b
ac
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
THEOREM 9.7
c 2 > a
2 + b 2
In a triangle, if c2 > a2 + b2, then the triangle is obtuse
ABC is obtuse
Converse of the Pythagorean Theorem9.3
Converse of the Pythagorean TheoremCONCEPT
SUMMARY
c2 < a2 + b2
Acutec2 = a2 + b2
Right
c2 > a2 + b2
Obtuse
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
AB
C
b
ac
A
BC b
ac
AC
B
b
ac
Converse of the Pythagorean Theorem9.3
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
With c as the longest side, fill in c2 = a2 + b2
Converse of the Pythagorean Theorem9.3
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
With c as the longest side, fill in c2 = a2 + b2
152 = 122 + 92
225 = 144 + 81
225 = 225
The triangle is a right triangle
Converse of the Pythagorean Theorem9.3
USE THE CONVERSE OF THE PYTHAGOREAN THEOREM
169 149
Not a Right Triangle
180 = 180
Right Triangle
Converse of the Pythagorean Theorem9.3
USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE
Make sure they can form a triangle, then compare c2 to a2 + b2
Converse of the Pythagorean Theorem9.3
USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE
Make sure they can form a triangle, then compare c2 to a2 + b2
Converse of the Pythagorean Theorem9.3
USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE
Make sure they can form a triangle, then compare c2 to a2 + b2
222 565_____9
Compare c2 with a2 + b2
5625_____81
222 ba_____c
Substitute
Multiply
c2 = a2 + b28181
Since c2 = a2 + b2, the triangle is a right triangle
Converse of the Pythagorean Theorem9.3
USE SIDE LENGTHS TO CLASSIFY TRIANGLES BY THEIR ANGLE MEASURE
12, 16, 20
400 = 400
The triangle is a right triangle
1681 > 1664
The triangle is obtuse
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