Download inequalities in triangles

Geometry
5.5 ‐ Inequalities in Triangles
A. Corollary to the Triangle Exterior Angle Theorem The measure of the exterior angle of a triangle is greater than the measure of each of its remote interior angles
Angle 1 > Angle 2 and Angle 1 > Angle 3
3
2
1
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B.
Examples: Explain why Angle 1 is larger than Angle 2
2
1
3
3
1
2
2
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C. Theorems
• Theorem 5.10 ‐ if two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
• Theorem 5.11 ‐ it two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.
NOTE: In a triangle with three unequal sides and angles, the longest side would be opposite the largest angle, the middle side would be opposite the middle angle, and the shortest side would be opposite the smallest angle
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D. Examples. List the angles and sides of the following triangles in order from least to greatest. J
34
M
17
21
0
0
O
59
35
K
L
N
P
1100
23
29
Q
R
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E. Theorem 5.12 (IMPORTANT) ***
The Triangle Inequality Theorem ‐ the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Y
XY + YZ > XZ
YZ + ZX > YX
ZX + XY > ZY
X
Z
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Examples. F.
Can a triangle have sides with the given lengths 3 ft, 7 ft and 1.
8 ft? Explain
Can a triangle have sides with the given lengths 3 cm, 6 cm 2.
and 11 cm? Explain
3.
Can a triangle have sides with lengths 2 in, 2 in and 4 in? Explain
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4. A triangle has side lengths of 9 yd, and 11 yd. Describe the possible length of the third side with an inequality.
5. A triangle has side lengths of 9 m and 17 m. Describe the possible length of the third side with an inequality.
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5.5 HW p. 292 #s 1 ­ 7, 10 ­ 13, 16 ­ 20, 22 ­ 24, 42 ­ 44
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