8.1 – Lines and Angles
Defn:
Space: The region that extends in all direction indefinitely.
Plane: A flat surface without thickness that extends
indefinitely in two directions..
8.1 – Lines and Angles
Defn:
Line: A set of points extending indefinitely in opposite
directions.
l
A
Line AB

B
Line l
AB

Line Segment: A piece of a line that has two end points.
A

B

line segment AB
AB
Ray: A part of a line with one end point extending
indefinitely in one direction.
A

B

ray AB
AB
8.1 – Lines and Angles
Defn:
Angle: A two dimensional plane whose sides consist of two
rays that share the same end point. The shared point is called
the vertex.
A

B

x
C

Angle BAC
 BAC
Angle CAB
 CAB
Angle A
A
Angle x
x
8.1 – Lines and Angles
Identify each of the following figures.
CF
VE
 TBS
 SBT
B
YI
 THV
 VHT
H
8.1 – Lines and Angles
Use the given figure to answer the questions.
1
What are the name(s) of the
given angle?
What are the other names of angle x?
 BAC
 AEC
 CAB
 CEA
A
E
1
8.1 – Lines and Angles
Classifying Angles
Degree: A unit for measuring angles. The symbol denoting
degrees is a raised circle (45°).
Straight angle: Any angle that measures 180° (a straight line).
Right angle: Any angle that measures 90°.
Acute angle: Any angle whose measurement is between 0°
and 90°.
Obtuse angle: Any angle whose measurement is between 90°
and 180°.
8.1 – Lines and Angles
Classifying Angles
straight
right
acute
obtuse
obtuse
8.1 – Lines and Angles
Special Pairs of Angles
Complimentary angles: Two angles whose sum is 90°. They
are compliments of each other.
Supplementary angles: Two angles whose sum is 180°. They
are supplements of each other.
What is the compliment of 15°?
90 – 15 = 75°
What is the supplement of 95°?
180 – 95 =
85°
What is the supplement of 29°?
180 – 29 = 151°
What is the supplement of 80°?
180 – 80 = 100°
What is the compliment of 29°?
90 – 29 = 61°
8.1 – Lines and Angles
Calculating the Measure of an Angle
Given the figure below,
what is the measure of 1?
68°
Given the figure below, what is
the measure of CPD?
176°
23°
119°
68 – 23 = 45°
What type of angle is 45°?
acute
176 – 119 = 57°
What type of angle is 57°?
acute
8.1 – Lines and Angles
Lines in a Plane
Intersecting Lines: Lines in a plane that cross at a common
point. If two lines intersect, they create four angles.
1
2
4
3
Vertical angles: Of the four angles formed from two
intersecting lines, these are the two pairs of opposite angles.
The measures of the opposite angles are the same.
2 = 4
1 = 3
8.1 – Lines and Angles
Lines in a Plane
Parallel lines: Two or more lines in a plane that do not
l1
intersect.
line l line 2
l2
l1 l2
Perpendicular lines: Two lines in a plane that intersect at a 90°
angle.
l3
line 3  line 4
l3  l4
l4
8.1 – Lines and Angles
Lines in a Plane
Adjacent angles: Angle that share a common side.
DBC is adjacent to CBA as they
share the common side BC.
Adjacent angles formed from two intersecting lines are
supplementary.
1 + 2 = 180°
2 + 3 = 180°
1
2
4
3 + 4 = 180°
3
4 + 1 = 180°
8.1 – Lines and Angles
Lines in a Plane
Transversal lines: Any line that intersects two or more lines at
l3
different points.
The position of the angles
created by the transversal
line have specific names.
a b
d c
l1
l2
f
h g
e
Corresponding angles:
a & e, b & f, d & h, and
Alternate interior angles:
d & f and c & e
c & g
8.1 – Lines and Angles
Lines in a Plane
If two parallel lines are cut by a transversal, then:
(a) The corresponding angles are equal,
(b) The alternate interior angles are equal.
l1 l2
l3
a b
d c
f
h g
e
l1
l2
Corresponding angles:
a = e, b = f,
d = h, and c = g
Alternate interior angles:
d = f and
c = e
8.1 – Lines and Angles
Given the measure of one angle, calculate the measures of the
other angles.
1
2
4
3
m1 = 30°
m4 = 127°
m2 = 180 – 30 = 150°
m1 = 180 – 127 = 53°
m3 = 30°
m2 = 127°
m4 = 150°
m3 = 53°
8.1 – Lines and Angles
Given the measure of one angle, calculate the measures of the
other angles.
l1 l2
l3
a b
d c
l1
l2
f
h g
e
me = 98°
md = 82°
ma = 98°
mf = 180 – 98 = 82°
mb = 82°
mg = 98°
mc = 98°
mh = 82°
8.2 – Perimeter
Defn.
Perimeter: The perimeter of any polygon is the total distance
around it. The sum of the lengths of all sides of the polygon is
the perimeter.
Calculate the perimeter of each of the following:
The length of a rectangle is 32 centimeters and its width is 15
centimeters.
P = 32 + 32 + 15 + 15 = 94 cm
P = 2(32) + 2(15) = 94 cm
8.2 – Perimeter
Calculate the perimeter of each of the following:
18 meters
The figure is a rectangle with the given
measurements.
10 meters
P = 2(18) + 2(10) = 36 + 20 = 56 m
15 feet
9 feet
7 feet
14 feet
P = 7 + 15 + 9 + 14 = 45 ft
8.2 – Perimeter
Calculate the perimeter of each of the following:
12 inches
29 inches
17 inches
All angles in the figure are 90°.
22 inches
29 – 12 = 17 inches
17 + 22 = 39 inches
P = 29 + 17 + 12 + 22 + 17 + 39 = 136 in
8.2 – Perimeter
A rectangular lot measures 60 feet by 120 feet. Calculate the
cost of a fence to be installed around the perimeter of the lot if
the fence costs $1.90 per foot.
Calculate the perimeter.
P = 2(60) + 2(120) = 120 + 240 = 360 ft
Calculate the cost of the fence.
C = 360 · 1.90 = $ 684.00
8.2 – Perimeter
Circumference – the length around the edge of a circle.
r
d
Blue line = Diameter
Red line = Radius
d = 2r
C=d
or
C=2r
8.2 – Perimeter
C=d
Find the exact circumference
of a circle whose diameter is
20 yards.
C=d
or
C=2r
Find the approximate value of the
circumference of a circle whose
diameter is 7 meters. ( Use 3.14
as an approximation of .)
C =  20
C=d
C = 20 yds
C = 3.14 (20)
3.14
x 20
6280
2 decimal places
62.80 yds