Activity 7 Notes
PreAP Geometry Niven
Parallel lines: coplanar lines that never intersect.
You can also have parallel,
perpendicular, and skew
rays and segments.
Perpendicular lines: lines that intersect forming right angles.
Skew lines: non-coplanar lines that will never intersect.
W
T
Example of parallel lines:
⃡𝐴𝐸 & ⃡𝑍𝐺
or __________________
A
E
Example of perpendicular lines:
⃡𝑍𝐻 & 𝐻𝑌
⃡
or __________________
This is a rectangular right
prism
H
Y
Example of skew lines:
⃡ & ⃡𝑇𝑌
𝐴𝐸
or ________________
Z
G
That is just two examples of each
There are many more examples in the diagram of each pair of lines.
t
1
Transversal: Line that intersects two or more coplanar lines
in different points.
3
2
4
Same-Side Interior angles: a pair of angles that are between
the two lines and on the same side of the transversal.
n
5
Examples: ∡3 and ∡5 ________________ __________________
6
m
8
7
Alternate Interior angles: a pair of nonadjacent angles that
are between the two lines and on opposite sides of the
transversal.
Examples: ∡3 and ∡6
t
________________ __________________
1
Corresponding angles: a pair of nonadjacent angles that are
in the same position, but different intersection of two lines.
One will be in between two lines and one will be outside
the two lines.
Examples: ∡1 and ∡5
3
p
2
9
4
11
12
n
∡ 6 and ∡14
13
________________ __________________
Alternate Exterior angles: a pair of angles that lie outside
the two lines and on opposite sides of the transversal.
Examples: ∡1 and ∡8
10
________________ __________________
5
7
14
6
8
15
16
m
There may be more than 3 lines involved.
𝑙𝑖𝑛𝑒 𝑡 is the transversal of 𝑙𝑖𝑛𝑒𝑠 𝑛 and 𝑚, BUT
𝑙𝑖𝑛𝑒 𝑚 is the transversal of 𝑙𝑖𝑛𝑒𝑠 𝑡 and 𝑝.
Activity 7 Notes
PreAP Geometry Niven
When the lines that are being cut by the transversal are parallel to each other, then some interesting things start to
happen.
If parallel lines are cut by a transversal, then Same-Side Interior
angles are supplementary.
t
2
1
Since 𝑙𝑖𝑛𝑒 𝑛 ∥ 𝑙𝑖𝑛𝑒 𝑚, that means ∡3 and ∡5 are
n
If parallel lines are cut by a transversal, then Alternate Interior
angles are congruent.
4
3
m
5
7
_____________________________
Since 𝑙𝑖𝑛𝑒 𝑛 ∥ 𝑙𝑖𝑛𝑒 𝑚, that means ∡3 𝑎𝑛𝑑 ∡6 are
6
_______________________ Notation___________________________
8
If parallel lines are cut by a transversal, then Corresponding angles
are congruent.
Since 𝑙𝑖𝑛𝑒 𝑛 ∥ 𝑙𝑖𝑛𝑒 𝑚, that means ∡4 𝑎𝑛𝑑 ∡8 are
_______________________ Notation___________________________
If parallel lines are cut by a transversal, then Alternate Exterior
angles are congruent.
Since 𝑙𝑖𝑛𝑒 𝑛 ∥ 𝑙𝑖𝑛𝑒 𝑚, that means ∡2 𝑎𝑛𝑑 ∡7 are
_______________________ Notation___________________________
You can prove lines are parallel using the CONVERSE of each conditional statement above.
If Same-Side Interior angles are supplementary, then lines are parallel.
If Alternate Interior angles are congruent, then lines are parallel.
If Corresponding angles are congruent, then lines are parallel.
If Alternate Exterior angles are congruent, then lines are parallel.
The perpendicular postulate states that if given a line and a point not on the line, then there is exactly one line through
the point that is perpendicular to the given line.
Likewise, the parallel postulate states that if given a line and a point not on the line, then there is exactly one line through
the point that is parallel to the given line.
The perpendicular transversal theorem states that if a transversal is perpendicular to one of the two parallel lines, then it
is perpendicular to the other line.
A perpendicular bisector of a segment is a line (or part of a line) that intersects the segment at its midpoint to form right
angles.