Download Notes 4D Triangle Angles and Inequalities

Bell ringer
Identify each of the pictures as one of the following:
perpendicular bisector
angle bisector
altitude
median
midsegment
none of these
B
A
A
1
B
(
(
A
B
Notes 4D: Triangles and Inequalities
Vocabulary:
Theorem 5.10
If one side of a triangle is longer than another side,
then the angle opposite the longer side is larger than
the angle opposite the shorter side.
B
3
m<A > m<C
5
Order the angles from least to greatest.
E
23
12
D
11
F
C
A
Theorem 5.11
If one angle of a triangle is larger than another
angle, then the side opposite the larger angle is
longer than the side opposite the smaller angle.
D
Order the sides from least to greatest.
B
37
55
E
60
40
EF > DF
F
88
A
C
List the sides in order from shortest to longest.
1.
2.
P
M
3.
L
B
C
45
Q
65
60
35
R
sm 55
N
md lg
sm A
md lg
sm md lg
List the angles in order form smallest to largest.
4.
X
4
5.
Y
6
R
16
9
12
V
14
T
Z
md U
16
12
8
sm 6.
S
W
lg
sm md lg
sm md lg
More Inequalities of
Theorem 5.13 Triangle Inequality
The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
9
8
8 + 9 > 7
9 + 7 > 8
8 + 7 > 9
17 > 7 True
16 > 8 True
15 > 9 True
7
Can a triangle have the side lengths listed below? Justify your answer.
1. 17,1,17
+ > + > + > A triangle? Yes / No.
2. 19,5,3
+ > + > + > A triangle? Yes / No.
Finding possible lengths of a 3rd side
A triangle has one side of 12 inches and another side of 16 inches.
Describe the possible lengths of the third side.
Between:
< x <
Two sides of a triangle are given, describe the possible lengths of the third side.
3. 9 inches
and 25 inches
1. 2 centimeters
and 5 centimeters
Between:
Between:
< x <
< x <
2. 4 feet
and 10 feet
4. 7 inches
and 12 inches
Between:
Between:
< x <
< x <
Finding possible values of "x"
5.
Look at the triangle below:
x-2
meters
10
meters
12 meters
What are the possible values of x? Between:
< x <
6.
Look at the triangle below:
8 miles
2x+2
meters
4 mile
What are the possible values of x? Between:
< x <
Sketch the Isosceles Triangle
You are given a 12 inch piece of wire. You want to form an isosceles
triangle so that the length of each side is a whole number.
1. Sketch two possible isosceles triangles and label each side.
You are given a 31 inch piece of wire. You want to form an isosceles
triangle so that the length of each side is a whole number.
2. Sketch two possible isosceles triangles and label each side.
Assignment
Worksheet 4D
# 1­27 all
# 28­40 even