# Slide 1 - ED2NET by ewghwehws

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```									    Geometry

Lines and Angles

CONFIDENTIAL   1
Warm Up
Find the circumference and area of each circle.

1)                             2)
80 cm                       3.8 m

CONFIDENTIAL                     2
Parallel, perpendicular and skew lines

Pairs of lines can relate to each other in four different
ways: intersecting lines, parallel lines, perpendicular
lines and skew lines. These concepts are useful for
understanding and solving various geometry
problems.

CONFIDENTIAL                          3
Parallel, perpendicular and skew lines

Parallel lines (||) are lines that never intersect i.e. they
are coplanar. The distance between the two lines is
fixed and the two lines go in the same direction.
In the figure, AB || EF and EG || FH.

A                   B

E                F

C                  D

G                H

CONFIDENTIAL                         4
Parallel, perpendicular and skew lines

Perpendicular lines (|)are lines that intersect at one point
and form a 90° angle i.e. two different straight lines on
the same plane in two different directions who meet each
other at only right angles are called Perpendicular Lines.
In the figure, AB | AE and EG | GH.

A                  B

E               F

C                  D

G               H

CONFIDENTIAL                           5
Parallel, perpendicular and skew lines

Skew lines are not coplanar. Skew lines only happen in
space. Skew lines never intersect because they are not on
the same plane. Skew lines are difficult to draw because
they exist in the three dimensional space.
In the figure, AB and EG are skew.

A                  B

E               F

C                  D

G               H

CONFIDENTIAL                        6
Parallel, perpendicular and skew lines

Parallel planes are planes that do not intersect.
In the figure, plane ABE || plane CDG.

A                B

E              F

C                D

G              H

CONFIDENTIAL                      7
Identifying types of lines and planes
Identify each of the following:

A) A pair of parallel segments.
KN || PS
K        L
B) A pair of skew segments.
LM || RS                                N        M

C) A pair of perpendicular segments.          P        Q
MR | RS
S        R

D) A pair of parallel planes.
plane KPS || plane LQR.

CONFIDENTIAL                    8
Referring to the figure, we can conclude:

AB is perpendicular to CL and CIB is 90°
•KE intersects IB at point J
•GH is parallel to AB
•KD is perpendicular to MH and KLH is 90°
•IL intersects JM at point K
•EF intersects GL at point M, intersects IL at point K and IB at point J

CONFIDENTIAL                         9
Now you try!

Identify each of the following:

C       D
1a) A pair of parallel segments
B       E
1b) A pair of skew segments

1c) A pair of perpendicular segments         G       H

1d) A pair of parallel planes            F       J

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Angle pairs formed by a transversal

A transversal is a line that intersects two coplanar lines at
two different points. The traversal t and the other two
lines r and s form eight angles.

exterior angles

interior angles

exterior angles

CONFIDENTIAL                         11
Corresponding angles are created where a transversal
crosses other (usually parallel) lines. The corresponding
angles are the ones at the same location at each
intersection i.e. angle 1 and angle 5.

Corresponding angles

CONFIDENTIAL                          12
Alternate interior angles are created where a transversal
crosses two (usually parallel) lines. Each pair of these
angles are inside the parallel lines, and on opposite sides
of the transversal i.e. angle 3 and angle 5.

Alternate interior angles

CONFIDENTIAL                            13
Alternate exterior angles are created where a transversal
crosses two (usually parallel) lines. Each pair of these
angles are outside the parallel lines, and on opposite sides
of the transversal i.e. angle 1 and angle 7.

Alternate exterior angles

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Same side interior angles crosses two (usually
parallel) lines. Each pair of interior angles are inside
the parallel lines, and on the same side of the
transversal. i.e. angle 3 and angle 6.

Same side interior angles

CONFIDENTIAL                          15
Classifying pairs of angles
Give an example of each angle pair.

A) Corresponding angles
Angle 4 and angle 8

B) Alternate interior angles
Angle 4 and angle 6

C) Alternate exterior angles
Angle 2 and angle 8

D) Same side interior angles
Angle 4 and angle 5

CONFIDENTIAL              16
Now you try!

Give an example of each angle pair.

2a) Corresponding angles

2b) Alternate interior angles

2c) Alternate exterior angles

2d) Same side interior angles

CONFIDENTIAL               17
Identifying angle pairs and transversals
Identify the transversal and classify each angle pair.

A) Angle 1 and angle 5
transversal: n; Alternate interior angles
4
l

B) Angle 3 and angle 6                                  5
transversal: m; Corresponding angles
6

C) Angle 1 and angle 4                          m           n
transversal: l; Alternate exterior angles

CONFIDENTIAL                         18
Now you try!

3) Identify the transversal and classify the angle pair   2
and 5 in the diagram.

4
l

5
6

m            n

CONFIDENTIAL                           19
Assessment

Identify each of the following:

B       C
1) A pair of perpendicular segments
A       D
2) A pair of skew segments

3) A pair of parallel segments               F       G

4) A pair of parallel planes             E       H

CONFIDENTIAL               20
Give an example of each angle pair.

5) Alternate interior angles

6) Alternate exterior angles

7) Corresponding angles

8) Same side interior angles

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Identify the transversal and classify each angle pair.

m
9) Angle 1 and angle 2
n
10) Angle 2 and angle 3
4
11) Angle 2 and angle 4                     5

12) Angle 4 and angle 5                     3
p

CONFIDENTIAL                            22
Let’s review

Parallel, perpendicular and skew lines

Parallel lines (||) are lines that never intersect i.e. they
are coplanar. The distance between the two lines is
fixed and the two lines go in the same direction.
In the figure, AB || EF and EG || FH.

A                   B

E                F

C                  D

G                H

CONFIDENTIAL                         23
Parallel, perpendicular and skew lines

Perpendicular lines (|)are lines that intersect at one point
and form a 90° angle i.e. two different straight lines on
the same plane in two different directions who meet each
other at only right angles are called Perpendicular Lines.
In the figure, AB | AE and EG | GH.

A                  B

E               F

C                  D

G               H

CONFIDENTIAL                       24
Parallel, perpendicular and skew lines

Skew lines are not coplanar. Skew lines only happen in
space. Skew lines never intersect because they are not on
the same plane. Skew lines are difficult to draw because
they exist in the three dimensional space.
In the figure, AB and EG are skew.

A                  B

E               F

C                  D

G               H

CONFIDENTIAL                        25
Parallel, perpendicular and skew lines

Parallel planes are planes that do not intersect.
In the figure, plane ABE || plane CDG.

A                B

E              F

C                D

G              H

CONFIDENTIAL                      26
Angle pairs formed by a transversal

A transversal is a line that intersects two coplanar lines at
two different points. The traversal t and the other two
lines r and s form eight angles.

exterior angles

interior angles

exterior angles

CONFIDENTIAL                         27
Corresponding angles are created where a transversal
crosses other (usually parallel) lines. The corresponding
angles are the ones at the same location at each
intersection i.e. angle 1 and angle 5.

Corresponding angles

CONFIDENTIAL                          28
Alternate interior angles are created where a transversal
crosses two (usually parallel) lines. Each pair of these
angles are inside the parallel lines, and on opposite sides
of the transversal i.e. angle 3 and angle 5.

Alternate interior angles

CONFIDENTIAL                            29
Alternate exterior angles are created where a transversal
crosses two (usually parallel) lines. Each pair of these
angles are outside the parallel lines, and on opposite sides
of the transversal i.e. angle 1 and angle 7.

Alternate exterior angles

CONFIDENTIAL                        30
Same side interior angles crosses two (usually
parallel) lines. Each pair of interior angles are inside
the parallel lines, and on the same side of the
transversal. i.e. angle 3 and angle 6.

Same side interior angles

CONFIDENTIAL                          31
You did a great job
today!

CONFIDENTIAL    32

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