Perpendicularity

1
Lesson 2.1

• Perpendicularity

Complements Supplements
Lesson 2.2
2
Perpendicular lines, rays or segments that
intersect at right angles.
?
Symbol for perpendicular
X
B
b
A
B
a
A
D
Y
AB
BD
?
a
?
b
XY
AB
?
3
If ltB is a right angle, then AB BC
?
A
C
B
Cant assume unless you have a right angle or
given.
?
4
A
D
Given AB BC DC BC Conclusion ltB ltC
?
?

C
B
Statement Reasons

1. AB BC
2. ltB is a right lt.
3. DC BC
4. ltC is a right lt.
5. ltB ltC

?

• Given
• If 2 segments are , they form a right lt.
• Given.
• If 2 segments are , they form a right lt.
• If lts are right lts, they are .

?
?
?


5
J
Given KJ KM ltJKO is 4 times as
large as ltMKO Find mltJKO
?
O
4x
x
M
K
Solution Since KJ KM, mltJKO mltMKO
90. 4x x 90 5x 90 x
18 Substitute 18 for x, we find that mltJKO 72.
?
6
y axis
Given EC ll x axis CT ll y axis Find the
area of RECT
C (7, 3)
321 123
E
x axis
-3 -2 -1 1 2 3
R (-4,-2)
T
Solution The remaining coordinates are T (7,
-2) and E (-4, 3). So RT 11 and TC 5 as
shown. Area base times height. A bh
(11)(5) 55 The area of RECT is 55 square
units.
7
Complementary Angles

• Complementary angles are two angles whose sum is
  90.
• Each of the two angles is called the complement
  of the other.

40
A
B
50
ltA ltB are complementary.
8
More Complementary Angles

• ltC is complementary to ltE.

C
60
J
F
6340
30
2620
D
E
G
H
ltFGJ is the complement of ltJGH.
9
Supplementary Angles

• Supplementary angles are two angles whose sum is
  180 (a straight angle).
• Each of the two angles is called the supplement
  of the other.

K
130
50
J
ltJ ltK are supplementary.
10

• Given Diagram as shown
• Conclusion lt1 is supplementary to lt2

1
2
A
B
C
Statement Reasons

1. Diagram as shown.
2. ltABC is a straight angle.
3. lt1 is supplementary to lt2.

1. Given
2. Assumed from diagram
3. If the sum of two lts is a straight lt, they are
   supplementary.