Download Note Sheet 5-3

Geometry 5-3 Inequalities in One Triangle
Consider a triangle. If we extend one of the sides, the
angle we form is called an exterior angle
. The two
angles inside the triangle that are not adjacent to the
exterior angle are its remote interior angles
.
Theorem 5.8 - Exterior Angle Theorem: The measure
of an exterior angle of a triangle is greater than the
measure of either of its corresponding remote interior
angles.
Name all angles that have measures less than 1.
4
3
1 2
4
Angle 1
is an exterior angle for the
triangle. Angles 3 and 4
are the
remote interior angles for angle 1 .
Theorem 5.9: If one side of a triangle is longer than
another side, then the angle opposite the longer side
is greater than the angle opposite the shorter side.
Theorem 5.10: If one angle of a triangle is greater
than another angle, then the side opposite the greater
angle is longer than the side opposite the lesser angle.
Short version: Bigger angle goes with bigger side;
smaller angle goes with smaller side.
2
5
3
7
1 8
3, 4, 5, 6
6
List the angles of ABC in order from smallest
to largest.
A
C
4.8
3.7
B
C
A
7
B
List the sides of WXY in order from largest to smallest.
Y
56
W
45
X = 180 - 56 - 45 = 79
X
WY
XW
YX