M 1312
Section 1.6
1
Relationships: Perpendicular Lines
Definitions:
 A plane is a two dimensional geometric object. It has infinite length and infinite
width but no thickness.
Parallel lines are lines that lie in the same plane but do not intersect. (Symbol || )

Perpendicular lines are two lines that meet to form congruent adjacent angles.
(Symbol 
.
Theroem: If two lines are perpendicular, then they meet to form right angles.
Given: AB  CD intersecting at E.
Prove: AEC is a right angle
Statements
Reasons
1. AB  CD intersecting at E.
1.
2.
3.
4.
5.
6.
AEC  CEB
mAEC  mCEB
AEB is a straight angle
mAEC  mCEB  AEB
mAEC  mCEB  180
mAEC  mAEC  180 or
2(mAEC)  180
8. mAEC  90
9. AEC is a right angle
2.
3.
4.
5.
6.
7.
7.
8.
9.
Table 1.8
Relation
Object Related
Example
Is equal to
numbers
2+3=5
Is greater than
numbers
7>5
Is perpendicular to
lines
Is complementary to
angles
n m
1 is comp to  2
M 1312
Section 1.6
Is congruent to
line segments
Is a brother
people
2
AB  CD
Mike is brother of Tom
Properties:
Reflexive property: aRa(5 = 5, equality of numbers has a reflexive property).
Symmetric property: If aRb, then bRa. (If n  m , then m  n , perpendicular lines have the
symmetric property).
Transitive property: If aRb and bRc, then aRc, (If m1  m 2 and m 2  m 3 , then
m1  m 3 , congruence of angle is transitive).
Example 2: Given the line segment
A
B
C
D
a. An example of reflexive property:
b. An example of the transitive property:
c. An example of the symmetric property:
Example 3: G i v e n : ∠
a n d ∠
∠
are complements.
are complementary, ∠
Use transitive property to show that ∠
C
A
D
B
E
≅ ∠
and
Math 1312 Popper 1 A D Use for questions 1 and 2: C B BD bisects ∠
. If ∠
3
25 and ∠
12
Popper 1: Question 1. Find the ∠
A. 18° B. 29° C. 31° D None of these Popper 1: Question 2: Find the ∠
. A. 58° B. 62° C. 36° D None of these Use for questions 3 and 4: Given: 3
1 2 If ∠1
7
3 and m∠2
2
4
12 Popper 1: Question 3 Find the measure of m∠2 . A. 18° B. 48° C. 26° D None of these Popper 1: Question 4: Find the ∠3 A. 132° B. 162° C. 154° D. None of these Popper 1: Question 5: If AB =BD and BD = BC, then AB = BC. A. Reflexive B. Distributive C. Transitive D. None of these 7