Transcript CHAPTER 6: Inequalities in Geometry

CHAPTER 6: Inequalities in
Geometry
Section 6-4:
Inequalities for One Triangle
THEOREM 6-2
Theorem 6-2:
If one side of a triangle is longer than a
second side, then the angle opposite the
first side is larger than the angle opposite
the second side.
THEOREM 6-3
Theorem 6-3:
If one angle of a triangle is larger than a
second angle, then the side opposite the
first angle is longer than the side opposite
the second angle.
COROLLARIES TO TH. 6-3
Corollary 1
The perpendicular segment from a point to a
line is the shortest segment from the point
to the line.
Corollary 2
The perpendicular segment from a point to a
plane is the shortest segment from the
point to the plane.
THEOREM 6-4
Theorem 6-4: The Triangle Inequality
The sum of the lengths of any two sides of a
triangle is greater than the length of the
third side.
PRACTICE
H
Name the largest angle
and the smallest angle of
the triangle.
10
6
I
8
J
Largest angle: I
Smallest angle: J
Complete With <, =, or >.
Given: ∆ ABC is a right triangle with the measure of angle C = 90.
Conclusions:
1. m∕_C
>
1. m ∕_A
2. m ∕_C
=
2. m ∕_A + m ∕_B
3. AC
<
3. AB
PRACTICE
The lengths of two sides Then, the length of the third
side must be greater than
of a triangle are:
___ but less than ___.
1. 8 and 13
1. 5, 21
2. 10 and 17
2. 7, 27
3. 3 and 12
3. 9, 15
Is it possible for a triangle to have sides
with the lengths indicated?
1. 6, 8, 10
1. Yes
2. 3, 4, 8
2. No
3. 2.5, 4.1, 5.0
3. Yes
4. 4, 6, 2
4. No
5. 6, 6, 5
5. Yes
Name the largest angle and the smallest
angle of the triangle.
B
1.
25
1. Largest: A
Smallest: C
29
A
C
26
R
2.
12
11
Q
13
S
2. Largest: R
Smallest: Q
CLASSWORK/HOMEWORK
CLASSWORK: PG. 221: CE 1-12
HOMEWORK: 6.3-6.4 WORKSHEET