Math II 7.5Parallel Lines and Transversals

ActivityLook at your assignment.

Activityuse a straight edge to draw a line that cuts through the first

pair of lines.

ActivityYou have made 8 angles!

ActivityUse your protractor to

measure and record the size of each angle.

ActivityRepeat this process with the Second set of parallel lines on

your worksheet

ActivityWith the 3rd set of lines

Start by drawing a line through them.

But this time we won’t use your protractor.

ActivityPick a symbol. # θ ♥ ☺♥ ♥ ♫

Any symbol you likeIt must be school appropriate!

ActivityDraw that symbol in one of the

angles.Now draw it in any other angle

that would have the same measure.

ActivityPick a different symbol.

$ & Any symbol you like

It must be school appropriate!

ActivityDraw that symbol in one of the

angles that does not have a symbol.

Now draw it in any other angle that would have the same

measure.

ActivityDo you notice any patterns?

Do you think this will always work?

So your last picture...

should look something like this...

1 2

3 4

5 6

7 8

TransversalThe line you drew has a

special name…It is a transversal.

Lines cut by a transversal may or may not be parallel.

98 percent of what we do in Math with transversals will involve parallel Lines

You will know they are parallel because they will tell you, or they will draw an extra arrow on the lines

Transversals can intersect any number of lines.

When a transversal intersects a line, four angles are formed

1 2

3 4

angles across from each other are called Vertical Angles.

1 2

3 4

∠1 and ∠4 are a pair of vertical angles∠2 and ∠3 are a pair of vertical angles

Based on your discoveries: What can you say about vertical angles?

1 2

3 4

When a transversal intersects two lines, eight angles are formed

1 2

3 4

5 6

7 8

These are called interior angles

3 4

5 6

These are called exterior Angles

1 2

7 8

Corresponding angles are angles in similar locations

1 2

3 4

5 6

7 8

Based on your discoveries: What can you say about corresponding angles?

1 2

3 4

5 6

7 8

Alternate interior Angles

3 4

5 6

Based on your discoveries: What can you say about alternate interior angles?

3 4

5 6

Alternate exterior Angles

1 2

7 8

Based on your discoveries: What can you say about alternate exterior angles?

1 2

7 8

Consecutive interior Angles

3 4

5 6

Based on your discoveries: What can you say about Consecutive interior angles?

3 4

5 6

Things to know:Vertical angles are always

Congruent

Things to know:If the lines are parallel then:

Corresponding Angles areCongruent

Things to know:If the lines are parallel then: Alternate Interior Angles are

Congruent

Things to know:If the lines are parallel then: Alternate Exterior Angles are

Congruent

Things to know:If the lines are parallel then:

Consecutive Interior Angles areSupplementary

Quick summary:

If lines are parallel, then

All ’s are congruent

All ‘s are congruent

+ = 180