section 5.5 inequalities in one triangle. theorem 5.10 if one side of a triangle is longer than...
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Section 5.5
Inequalities in One Triangle
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Theorem 5.10
• If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
15
12
A
B
A B
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THEOREM 5.11
• If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle
60 o
45 o
Side 1
Side 2Side 1 > Side 2
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Write the sides/angles in order from least to greatest.
A
B
C
D
F
E
33
22
15
63
32
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Is PQ>8? Is RQ<8?
P
Q
R61
57
8
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Exterior Angle Inequality
• The measure of an exterior angle of a triangle is greater then the measure of either of the two nonadjacent interior angles.
1
A
B
<1 is greater than <A
<1 is greater than <B
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What are the possible angle measures of <A?
A
42
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Triangle Inequality
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
BC
A
AB + BC >AC
AC + BC > AB
AB + AC > BC
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Is it possible to have a triangle with the given side lengths?
• 3, 8, 3• 6, 7, 12• 9, 5, 11• 8, 12, 20
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What are the possible lengths of the third side of the triangle?
• 8, 17, ?
• 12, 18, ?
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Write and solve the inequality PQ + QR > PR.
P
Q
R
3x-32x+1
3x+1