Chapter 2: Basic Geometric
Concepts and Basic Proofs
2.1 Perpendicularity
Symbol for perpendicular: 
Definition: Lines, rays, or
segments that intersect at
right angles are
perpendicular.
Perpendicular:


Lines, Rays, or Segments that intersect at right
angles
**In DE  EF the little mark
Examples:
inside the angle (L) indicates
a
J
<DEF is a right angle. **
E
H
b
G
D
a b
DE  EF
M
**This also means
JM  GH
m<DEF = 90°**
F
Can we assume a right angle??
NO!!!!!

Therefore, you cannot assume
perpendicularity from a diagram either.
A
In ABC it appears that AB  BC BUT, we
must be given this or be able to prove it, you
CANNOT ASSUME it.
B
C
J
Example 1:
Given:
4x
K
O
x
M
KJ  KM
mJKO is 4 times as large as mMKO
Find:
mJKO
**Since KJ  KM
, mJKO  mMKO  90 **
4x  x  90
5x  90
x  18
mJKO  4x
 4 18
 72
Example 2:
Given:
AB  BC
A
D
B
C
DC  BC
Prove: B  C
Reason
Statement
1.
AB  BC
1.
Given
2.
DC  BC
<ABC is right angle
2.
If 2 segs. are perpendicular, then they
form a right angle
<DCB is right angle
3.
B  C
3.
If 2 angles are right angles, then they
are congruent. (or just Theorem 1)
Examples of Perpendicularity
The x-y axes
Quadrant
Numbers?
Examples of Perpendicularity
“T-Square”
Perpendicular Planes
Triangle Altitudes
Definition:
Two intersecting non-parallel
lines are called oblique lines.
Definition:
Two non-intersecting non-parallel
lines are called skew lines.