Download Exterior Angle Inequality

5.5
Triangle Inequalities
If two sides of a triangle are not congruent, then the ________________ lies opposite
the __________________________.
X
6
9
Z
Y
If two angles of a triangle are not congruent, then the __________________ lies
opposite the ______________________.
A
110°
30°
B
C
Example:
Can you find the longest or the shortest side?
45°
43°
55°
52°
Exterior Angle Inequality
The measure of an exterior angle of a triangle is greater than the measure of either of the 2 non-adjacent
interior angles.
A
m<1 is greater than _______
m<1 is greater than _______
1
B
Triangle Sides Inequality:
The sum of the lengths of __________________________ of a triangle
is greater than _______________________.
Are the following triangles possible?
Example 1:
sides 4, 8, 6
Check: the sum of the 2 shortest sides must be
greater than the 3rd side.
Example 2:
sides 2, 2, 4
Example 3:
sides 10, 7, 2
Example 4:
sides 6.5, 13.7, 7.4
Given 2 sides, find the possible values of the third side.
1)
7, 12
2)
10, 14
3)
a,b where a > b
4)
8, 11
5.6
Inequalities in two triangles
E
Hinge Theorem
If
AB  DE, BC  EF
and mB  mE
D
F
then ____________________
B
A
E
Converse of the Hinge Theorem
If
C
AB  DE, BC  EF
and AC  DF
Then ________________
D
F
B
A
Example:
XY = ZY = 5
<XYW = 30°
C
X
<WYZ = 40°
Y
What can you conclude?
W
Z
Homework: TB p 348 14-22 even
TB p 367 6-16 even
TB p 376 10-18 even