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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. **In the little mark inside the angle (L) indicates
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Chapter 2: Basic Geometric Concepts and Basic Proofs
2.1 Perpendicularity
Definition: Lines, rays, or segments that intersect at
right angles are perpendicular.
Symbol for perpendicular:
Perpendicular:
Lines, Rays, or Segments that intersect at right angles Examples:
a
b
J
G
H
M
D
E
F
����a b J M GH
DE EF
**In the little mark inside the angle (L) indicates <DEF is a right angle. **
DE EF
**This also means
m<DEF = 90°**
Can we assume a right angle??
NO!!!!! Therefore, you cannot assume
perpendicularity from a diagram either.A
B C
In it appears that BUT, we must be given this or be able to prove it, you CANNOT ASSUME it.
ABC AB BC
Example 1:
Given:
is 4 times as large as
KJ KM����������������������������
m J KO m MKO
m J KOFind:
J
K
O
M
**Since , **KJ KM����������������������������
90m J KO m MKO
4 90x x 4m J KO x
5 90x 18x
4 18
72
4xx
Example 2:
Given: AB BC
DC BC
Prove: B C
A
B C
D
.1
AB BC
DC BC
.3 B C
Statement Reason
1. Given
2. <ABC is right angle
<DCB is right angle
2. If 2 segs. are perpendicular, then they
form a right angle
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.
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