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Parallel Lines and Transversals

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by

Damian Kusnierz

on 12 November 2013

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Transcript of Parallel Lines and Transversals

Parallel Lines and Transversals
transversals
- A line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.
transversals
Properties of parallel lines with transversals
Interior angles
1
2
3
4
Angles:
angle 1 = angle 4
angle 2 = angle 3
angles 1 and 2 are supp.
angles 3 and 4 are supp.
angles 3 and 1 are supp.
angles 4 and 2 are supp.
Exterior angles
1
2
3
4
~
~
Angles:
angle 1 = angle 4
angle 2 = angle 3
angles 1 and 2 are supp.
angles 3 and 4 are supp.
angles 3 and 1 are supp.
angles 4 and 2 are supp.
All angles
1
2
3
4
5
6
7
8
~
~
Angles:
angle 1 = angle 4 = angle 5 = angle 8

angle 2 = angle 3 = angle 6 = angle 7
Supplementary angles
angles 1 and 2, 3 and 4, 5 and 6, 7 and 8,
7 and 5, 8 and 6, 3 and 1, 4 and 2, 1 and 5,
2 and 6, 7 and 3, 8 and 4, 8 and 2, 1 and 7
Oreos!
You have an oreo, you are also very bored. You decide to cut it and measure all the angles. But after measuring the first angle, which was 66 , your protractor breaks. Don't ask how... Find all the other angles.
Oreos! continued.
66
o
2
3
4
5
6
7
8
Hint:
o
The Theorems
You have just used three theroms without even knowing you used them.
Alternate interior angles Theorem
If two lines cut by a transversal are parallel, then alternate interior angles are congruent.
Alternate exterior angles Theorem
If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.
Same-side interior angles Theorem
If two lines cut by a transversal are parallel, then same-side interior angles are supp.
Now try this!
Open your book to page 160 and do #22-27.
A
B
C
D
E
80
25
50
o
o
o
DONE!
~
~
~
~
~
~
Listen to the teachers on whether or not to take notes.
corresponding angles
1
2
3
4
5
6
7
8
Angles:
angles 1 = angle 5
angles 2 = angle 6
angles 7 = angle 3
angles 8 = angle 4
Corresponding angles postulate
If two lines cut by a transversal are parallel, then corresponding angles are congruent.
1
5
~
~
~
~
3
6
1
8
3
5
Full transcript