1. 5-2 Inequalities and Triangles

2. Exterior Angle Inequality Theorem
The measure of the exterior angle of a triangle is greater than either of its remote interior angles 2 1 3 4

3. Examples: Which angle has the greatest measure?1. 2. 5 4 5 4 1 2 3 1 2 3
a.) <1, <2, <3
b.) <2, <3, <5
c.) <1, <2, <3, <4, <5

4. Theorem 5.9
In a triangle, the larger angle (longer side) is opposite the longer side (larger angle) B S 65
4.8
3.6 40 75 C A U V
5.1
Since <C is larger, ____ is the
longest side and ____ is the shortest side
Since US is the shortest side,
<______ is the smallest angle
and
<______ is the largest angle

5. Example: Determine the relationship between each. Write <,> or =
<WXY____<XYW
<XZY_____<XYZ
<WYX____<XWY 12 X W 18 15 14 Y Z 17

6. Example:
List the sides of triangle MNO in order, longest to shortest if m<M=4x+20, m<N=3x+10 and m<O=3x-20
List angles of triangle KLM in order from least to greatest if KL=x-4, LM=x+4 and KM=2x-1 and the perimeter of the triangle is 27