Embed Size (px)
Citation preview
1
3.3 Parallel Lines and Transversals
2
transversal: a line that intersects two coplanar lines at different points.
t
exterior
exterior exterior
exterior
interiorinterior
p
q
t is a transversal
3
1 234
5 678
corresponding anglesare on the same side of the transversal and in the same position at each intersection.
The following are pairs of corresponding angles.
<1 and <5
<2 and <6
<3 and <7
<4 and <8
4
1 234
5 678
alternate interior anglesare on alternate sides of the transversal and in between the two lines.
The following are pairs of alternate interior angles.
<3 and <5
<4 and <6
5
1 234
5 678
alternate exterior anglesare on alternate sides of the transversal and outside of the two lines.
The following are pairs of alternate exterior angles.
<1 and <7
<2 and <8
6
1 234
5 678
sameside interior anglesare on the same side of the transversal and in between the two lines.
The following are pairs of same side interior angles.
<4 and <5
<3 and <6
7
Why do we have special names for these angles?
Because when the lines are parallel, certain relationships form.
8
If the lines are parallel, then
1.
2.
3.
4.
Remember, the following is always true even if the lines aren't parallel:
1.
2.
vertical angles are congruent
corresponding angles are congruent
alternate interior angles are congruent
alternate exterior angles are congruent
sameside interior angles are supplementary
linear pair are supplementary
1 23 4
5 67 8
9
If the lines are parallel, then
1.
2.
3.
4.
corresponding angles are congruent
alternate interior angles are congruent
alternate exterior angles are congruent
sameside interior angles are supplementary
These form three theorems and a postulate.
postulate
theorem
The names of each are on the next page.
10
Add these to your list of reasons in proofs:
• Corresponding Angles Postulate• Alternate Interior Angles Theorem• Alternate Exterior Angles Theorem• Sameside Interior Angles Theorem
11
D C
BA1 2
34
Notice a parallelogram has lines being cut by transversals
alternate interior angles
same side interior angles
Can you find any more special pairs?
12
Homework: wkst
You should be able to:1. Define transversal, alternate interior, alternate exterior, sameside interior and corresponding angles2. Identify angles pairs on a diagram
