8.1 – Lines and AnglesDefn:

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 AnglesDefn:

Ray: A part of a line with one end point extending indefinitely in one direction.

A

Line: A set of points extending indefinitely in opposite directions.

Line Segment: A piece of a line that has two end points.

B

Line AB Line lABl

A

Bline segment AB AB

A

Bray AB AB

8.1 – Lines and AnglesDefn:

Angle: A two dimensional plane whose sides consist of two rays that share the same end point. The shared point is called the vertex.

Angle BACA B

x

C

BAC

Angle CAB CAB

Angle A A

Angle x x

8.1 – Lines and AnglesIdentify each of the following figures.

VE YICF

SBT TBS

B

VHT THV

H

8.1 – Lines and AnglesUse the given figure to answer the questions.

BAC

CAB

A

AEC

CEA

E

What are the name(s) of the given angle?

1

1

What are the other names of angle x?

8.1 – Lines and AnglesClassifying Angles

Right angle: Any angle that measures 90°.

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).

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 AnglesClassifying Angles

straight acute obtuse

right obtuse

8.1 – Lines and AnglesSpecial Pairs of Angles

What is the compliment of 15°?

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 supplement of 80°?

90 – 15 = 75° 180 – 80 = 100°

What is the supplement of 95°?

180 – 95 = 85°

What is the compliment of 29°?

90 – 29 = 61°

What is the supplement of 29°?

180 – 29 = 151°

8.1 – Lines and AnglesCalculating the Measure of an Angle

What type of angle is 57°?

Given the figure below, what is the measure of 1?

acute

68 – 23 =

What type of angle is 45°?

acute

45°

68°

23°

176 – 119 = 57°

119°

176°

Given the figure below, what is the measure of CPD?

8.1 – Lines and AnglesLines in a Plane

1 = 3

Intersecting Lines: Lines in a plane that cross at a common point. If two lines intersect, they create four angles.

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.

1 23

4

2 = 4

8.1 – Lines and AnglesLines in a Plane

Parallel lines: Two or more lines in a plane that do not intersect.

Perpendicular lines: Two lines in a plane that intersect at a 90° angle.

line l line 2

l1 l2

l1

l2

l3

l4

line 3 line 4

l3 l4

8.1 – Lines and AnglesLines in a Plane

1 + 2 = 180°

Adjacent angles: Angle that share a common side.

Adjacent angles formed from two intersecting lines are supplementary.

1 23

4

DBC is adjacent to CBA as they share the common side BC.

2 + 3 = 180°

3 + 4 = 180°

4 + 1 = 180°

8.1 – Lines and AnglesLines in a Plane

Transversal lines: Any line that intersects two or more lines at different points.

The position of the angles created by the transversal line have specific names.

l1

l2

l3

a bcd

e fgh

Corresponding angles:

a & e, b & f, d & h, and c & gAlternate interior angles:

d & f and c & e

8.1 – Lines and AnglesLines in a Plane

If two parallel lines are cut by a transversal, then:

l1 l2

l1

l2

l3

a bcd

e fgh

(a) The corresponding angles are equal,

(b) The alternate interior angles are equal.

Corresponding angles:

a = e, b = f,

Alternate interior angles:

d = f and

d = h, and c = g

c = e

8.1 – Lines and Angles

1 23

4

Given the measure of one angle, calculate the measures of the other angles.

m1 = 30°

m2 =

m3 =

m4 =

30°

180 – 30 = 150°

150°

m4 = 127°

m1 =

m2 =

m3 =

53°180 – 127 =

127°

53°

8.1 – Lines and Angles

l1 l2

l1

l2

l3

a bcd

e fgh

Given the measure of one angle, calculate the measures of the other angles.

me = 98°

ma =

mb =

mc =

82°

98°

98°

md =

mf =

mg =

mh =

98°

180 – 98 = 82°

82°

82°

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.

Defn.

8.2 – 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 + 15+ 32 + 15 = 94 cm

P = 2(32) + 2(15) = 94 cm

8.2 – PerimeterCalculate the perimeter of each of the following:

The figure is a rectangle with the given measurements.

P = 7 + 14+ 15 + 9 = 45 ft

P = 2(18) + 2(10) = 56 m

18 meters

10 meters

36 + 20 =

15 feet

7 feet 9 feet

14 feet

8.2 – PerimeterCalculate the perimeter of each of the following:

All angles in the figure are 90°.

P = 29 + 22+ 17 + 12 + 17 + 39 = in

22 inches

17 inches

136

12 in

ches

29 in

ches

29 – 12 = 17 inches

17 + 22 = 39 inches

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.

8.2 – Perimeter

Calculate the perimeter.

Calculate the cost of the fence.

C = 360 · 1.90 $ 684.00=

P = 2(60) + 2(120) = 360 ft+ 240120 =

Blue line = Diameter

Red line = Radius

d = 2r

Circumference – the length around the edge of a circle.

C = d

r

d

C = 2 r

or

8.2 – Perimeter

Find the exact circumference of a circle whose diameter is 20 yards.

628020

yds

x3.14

2 decimal places

62.80

C = d C = 2 ror

C = 3.14 (20)

8.2 – Perimeter

Find the approximate value of the circumference of a circle whose diameter is 7 meters. ( Use 3.14 as an approximation of .)C = d

C = 20

C = 20 yds

C = d