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Lines and Angles . B. A. D. l. C. m. PARALLEL LINES. Def: line that do not intersect. Illustration: Notation: l || m AB || CD. Examples of Parallel Lines. Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking

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parallel lines

B

A

D

l

C

m

PARALLEL LINES
  • Def: line that do not intersect.
  • Illustration:
  • Notation:l || mAB|| CD
slide3

Examples of Parallel Lines

  • Hardwood Floor
  • Opposite sides of windows, desks, etc.
  • Parking slots in parking lot
  • Parallel Parking
  • Streets: Laramie & LeClaire
perpendicular lines

m

n

PERPENDICULAR LINES
  • Def: Lines that intersect to form a right angle.
  • Illustration:
  • Notation:m n
  • Key Fact: 4 right angles are formed.
slide5

Ex. of Perpendicular Lines

  • Window panes
  • Streets: Belmont and Cicero
angles
Angles

Two rays or line segments that meet at a point form an angle. The point where the rays meet is called the vertex of the angle.

We measure the size of an angle using degrees.

two ways to label angles
Two ways to label angles:

1. by giving the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta), or sometimes a number

2. or by the three letters on the shape that define the angle, with the middle letter being the vertex.

Example angle "a" is "BAC” (or

“CAB”),

and angle "θ" is "BCD” (or “DCB”)

measuring angles
Measuring Angles
  • This is one degree:
  • A Full Circle is 360°
  • Half a circle is 180°(called a straight angle)
  • Quarter of a circle is 90°(called a right angle)
types of angles
Types of Angles

Angle Names:

Acute – less than 90 degrees

Right – exactly 90 degrees (indicated on the GED by a square in the corner of the angle)

Obtuse – more than 90 degrees

Straight – exactly 180 degrees

complementary angles
Complementary Angles

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

One of the complementary angles is said to be the complement of the other.

vertical angles
Vertical Angles

Two straight lines crossing create vertical angles. Vertical angles (such as <BEC and <AED) have equal angle measurements.

In the diagram below, <AEB and <DEC are also vertical and therefore equal angles.

corresponding angles
Corresponding Angles
  • A line going through two parallel lines creates corresponding angles.
  • Corresponding angles (such as <D and <B) have equal measurements.
  • In the diagram below, <C and <A are also corresponding and therefore equal angles.
slide14

Corresponding

5

6

4

7

8

3

2

t

1

slide15

Corresponding

4 and 2

3 and 1

5 and 7

6 and 8

5

6

4

7

8

3

2

t

1

angle measurements
Angle Measurements
  • If <VNL measures 130°, what is the measurement of <UNB?
angle measurements1
Angle Measurements
  • If <VNL measures 130°, what is the measurement of <UNB?
  • <VNL and <UNB are

vertical angles. Therefore,

their measurements are the same.

<UNB = 130°

angle measurements2
Angle Measurements
  • If <VNL measures 130°, what is the measurement of <LNB?
angle measurements3
Angle Measurements
  • If <VNL measures 130°, what is the measurement of <LNB?
  • <VNL and <LNB are supplementary angles.
  • 180 – 130 = 50
  • <LNB = 50°
angle measurements4
Angle Measurements
  • If <SMP is a right angle and <ZMP measures 43°, what is the measurement of <ZMS?
angle measurements5
Angle Measurements
  • If <SMP is a right angle and <ZMP measures 43°, what is the measurement of <ZMS?
  • <ZMP and <ZMS are

complementary angles.

90 – 43 = 47

<ZMS = 47°

angle measurements6
Angle Measurements
  • <QFL is a straight angle. If <LFC measures 50°, what is the measurement of <QFC?
angle measurements7
Angle Measurements
  • <QFL is a straight angle. If <LFC measures 50°, what is the measurement of <QFC?
  • The angles are supplementary
  • 180 – 50 = 130
  • <QFC = 130°
angle measurements8
Angle Measurements
  • If <AKS is 38°, find the measurements of all of the other angles
if aks is 38 find the measurements of all of the other angles
If <AKS is 38°, find the measurements of all of the other angles
  • <EKR is vertical to <AKS,

so <EKR = 38°

  • <AKE is supplementary to

<EKR, so <AKE = 142° (180 – 38)

  • <RKQ is complementary to <EKR, so <RKQ = 52° (90 – 38)
  • Finally, <SKQ is supplementary to <EKQ, so it must measure 90° (180 – 90)
angle measurements9
Angle Measurements
  • If <NTF measures 125°, what are the measurements of the other angles?
if ntf measures 125 what are the measurements of the other angles
If <NTF measures 125°, what are the measurements of the other angles?
  • <NTF is supplementary to <RTN,

so <RTN must be 55° (180 – 125)

  • <FTY is vertical to <RTN and supplementary

to <NTF, so it must also be 55°

  • <RTY is vertical to NTF and supplementary to <FTY, so it must also measure 125°
  • <NTF corresponds with <KRT, so they have

the same measurements. <KRT = 125°

  • <TRU = 55° (corresponding to <FTY)
  • <XRU = 125° (corresponding to <RTY)
  • <XRK = 55° (corresponding to <RTN)
slide29

All the interior angles of any triangle will together add up to 180°

  • All the interior angles of any quadrilateral (square, rectangle, parallelogram, trapezoid) will add up to 360°
slide31

What is the measure of the missing angle, <BAC?

All triangles have interior angles totaling 180°,

So 180 – (52 + 48) gives us:

<BAC = 80°

slide33

Find the measure of the missing angle:

  • All quadrilaterals have

interior angles totaling 360°,

so, 360 – (68+106+126)

360 – 300 = 60

gives us:angle x measures 60°

lines and angles1
Lines and Angles
  • Pages 167 – 170 in the book
    • Check answers online
  • Pages 29-30 in the GED Practice Packet
    • Enter answers online