Download Geometry 5-2 Inequalities and Triangles

Geometry 5-2 Inequalities and Triangles
A. Angle Inequalities
1. Properties
a) Comparison Property
a < b, a = b, a > b
b) ______________Property
if a < b, and b < c, then a <c
c) Addition and _____________Properties
If a < b, then a + c < b + c
d) _______________Properties
if c > 0 and a < b, then a•c < b•c
2
2. Theorem 5-8 – Exterior Angle Inequality Theorem
If an angle is an exterior angle of a triangle, then it’s
measure is greater than the measure of either of its
corresponding remote interior angles.
m< 3 > m______
m< 3 > m______
1
3
Ex 1: Use the Exterior Angle Inequality Theorem to list all the angles that satisfy the
given conditions.
1
a) All angles whose measures are less than m < 8
2
3
4
b) All angles whose measures are greater than m < 2
B. Angle Side Relationships
1. Theorem 5-9 – If one side of a triangle is longer
than another side, then the angle opposite the longer
side has a greater measure than the angle opposite the
shorter side.
If CB > AB, then _____________
8
7
6
5
C
A
B
Ex 2: Determine the relationship between the measures of the given angles.
a) <RSU, <SUR
R
b) <TSV, <STV
5.2
5.3
c) <RSV, <RUV
S
3.6
2. Theorem 5-10 – If one angle of a triangle has
a greater measure than another angle, then the side
opposite the greater angle is longer than the side
opposite the smaller angle.
C
If m<A > m<C, then ___________________
A
HW: Geometry 5-2 p.252-254
18-34 even, 38-50 even, 55-59, 64-68
T
4.4
4.8
5.1
U
6.6
V
B