Download Section 5.5: Inequalities in Triangles

LEQ: How can use angle measures or side lengths to
make conclusions in triangles?
Solve the inequalities:
1.) 7x-13≤-20
2.) .5(4x-8)≥19
3.) 5x-3x-6x‹-20
4.) 8y-4y+11≤-33
5.) 8c+2c+7<-10-3
Activity on notes
B
A
D
C
E
F
Theorem 5-10
 If two sides of a triangle are not congruent, then the larger
angle lies opposite the longer side.
Theorem 5-11:
If two angles of a triangle are not congruent, then the longer
side lies opposite the larger angle.
Ex: List the sides of the angles from
longest to shortest
K
N
H
40
70
G
60
30
90
I
J
110
L
M
O
List the angles from smallest to
largest
Q
T
12
13
8
16
24
P
11
R
S
U
Activity on notes
 Draw triangles.
 Add up 2 sides of the triangle, how does the sum
compare to the 3rd number? Try 2 different sides…same
thing?
 Repeat this with the other examples.
 What can you conclude?
Thm. 5-12
 Triangle Inequality Thm.: The sum of the lengths of any
two sides of a triangle is greater than the length of the third
side.
Try examples a-c.
c.) If 2 sides are 5 and 12, what is the range for the 3rd
side?
Missing side= x
x+5>12 AND 12 +5 >x
Hwk: p. 292-293
 4-27 all, 35-37