Download 5:4 Inequalities for Sides and Angles of a Triangle

5:4 Inequalities for Sides and
Angles of a Triangle
Objective: Recognize and apply
relationships between sides and
angles of triangles
Theorem: 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.
C
EX.
7
A
12
9
B
List the angles from greatest
to least.
EX:
D
35°
55°
E
F
List the sides from shortest
to longest.
Theorem: 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
lesser angle.
EXAMPLE
1. Which is greater,
mCBD or mCDB?
C
15
D
2. Is mADB> mDBA?
8
3. Which is greater,
mCDA or mCBA?
A
16
12
10
B
PRACTICE
L
10
1. Name the angle with the
least measure in ▲LMN.
N
7
6
2. Which angle in ▲MOT
has the greatest
measure?
M
9
5
O
8
T
3. Name the greatest of the
six angles in the two
triangles, LMN and MOT.
EXAMPLE
1. Which side of ▲RTU
is the longest?
T
2. Name the side of
▲UST that is the
longest.
30º
110º
3. If TU is an angle bi sec tor ,
which side of RST is the
longest ?
R
U
S
PRACTICE
A
E
55º
D
30º
B
40º
100º
C
50º
1. What is the longest
segment in ▲CED?
2. Find the longest segment
in ▲ABE.
3. Find the longest segment
on the figure. Justify your
choice.
4. What is the shortest
segment in BCDE?
5. Is the figure drawn to
scale? Explain.
Exit Ticket
• Find the value of x and list the sides of
∆ABC in order for SHORTEST to
LONGEST if the angles have the indicated
measures.
m∠A = 12x - 9, m∠B = 62 – 3x ,
m∠C = 16x + 2