Download Inequalities and Triangles

Inequalities and Triangles
Sec: 5.6
Sol:G.5
Theorem 5.1 Mid-segment Theorem:
The segment connecting the midpoints of two
sides of a triangle is parallel to the third side
and is half the length of that side.
B
DE AC
D
A
E
C
1
DE  AC
2
Theorem 5.8 Exterior angle inequality
theorem:
If an angle is an exterior angle of a triangle, then
its measure is greater than the measure of
either of its corresponding remote interior
angles.
B
Ex: m4 > m2
m4 > m1
2
1
A
4
3
C
Theorem 5.9 Side – Angles
Relationship
If one side of the triangle is longer than another
side, then the angle opposite the longer side
has a greater measure then the angle opposite
the shorter side.
P
O
R
Ex: Determine the relationship between the
measures of the given angles.
R
5.2
U
a) RSU , SUR
b) TSV , STV
c) RSV , RUV
6.6
S
5.1
V
T
EX:
Ebony is following directions for folding a
handkerchief to make a bandana for her hair.
After she folds the handkerchief in half, the
directions tell her to tie the two smaller angles
of the triangle under her hair. If she folds it
with the dimensions shown, which two ends
should she tie?
Y
22.6
X
Z
Theorem 5.10 Angle – Side
Relationship
• 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.
P
R
Q
Section 5.4
Theorem 5.11 Triangle Inequality Theorem:
The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
A
All of the following must be true:
AB+BC>AC
BC+AC>AB
B
AC+AB>BC
C
*Theorem 5.11 is used to determine whether the three given segments can form a
triangle.*
Examples:
1.
2.
3.
4.
2,4,5
6.8, 7.2, 5.1
6.5, 6.5, 14.5
In Triangle PQR, PQ=7.2,and QR=5.2 Which
measure cannot be PR?
a) 7
b) 9
c) 11
d) 13
Find the range for the measure of the
third side.
1. 6 and 7
2. 5 and 2
3. 7 and 17
Distance Between a point and a line:
Theorem 5.12 : The perpendicular segment
from a point to a line is the shortest segment
from the point to the line.
P
EX: PQ is the shortest
segment from P to AB
A
Q
B
Corollary 5.1:
The perpendicular segment from a point to a
plane is the shortest segment from the point
to the plane. A
Which segment is the
shortest possible
distance from point A
to Plane P?
B
F
E
D
C
P
Suggested assignment
Classwork: Workbook pg 139-140 all
Homework: Pg 329 10-32 even