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Geometry

- Chapter 3 Using Parallel and Perpendicular Lines

3.1 Parallel Lines and Transversals

- Identify the angle pairs formed by parallel lines

and a transversal

What you know

- Parallel Lines

Topic 1 Parallel Lines and Skew Lines

- Parallel Lines that never touch and go in the

same direction

- Skew Lines Lines that never touch but do NOT go

in the same direction

j k

m n

AB is skew to SD

Examples

List all the pairs of Parallel Lines

List all pairs of skew lines

AB CD

AB is skew to ED

CA DB

AB is skew to EC

CD is skew to EB

CD is skew to EA

CA is skew to EB

CA is skew to ED

BD is skew to EC

BD is skew to EA

Topic 2 Transversals

- A transversal is a line that crosses any two

other lines

j is a transversal for l and k

Examples

What is the transversal for n and k?

What is the transversal for m and k?

m is the transversalit crosses both

n is the transversalit crosses both

Topic 3 Corresponding Angles

- Corresponding Angles Same positiondifferent

line

If n is the transversal

?5 is on the top left

?9 is on the top left

So ?5 and ?9 are corresponding angles

?4 and ?2 are corresponding angles

?10 and ?6 are corresponding angles

Example

If k is the transversal find all the pairs of

corresponding angles

?9 corresponds with

?6

?11 corresponds with

?7

?12 corresponds with

?8

?10 corresponds with

?5

Topic 4 Alternate Interior Exterior

If k is the transversal

- Alternate angles opposite side of the

transversal - Interior angles In between the two lines
- Exterior angles Outside the two lines

?4, ?3, ?6, ?5 are inside the other lines they

are INTERIOR

?1, ?2, ?8, ?7 are outside the other lines they

are EXTERIOR

?3, ?6 are on opposite sides of the

transversalthey are ALTERNATE INTERIOR

So are ?4 and ?5

?1, ?8 are on opposite sides of the

transversalthey are ALTERNATE EXTERIOR

So are ?2 and ?7

Topic 5 Consecutive Interior

If k is the transversal

- Consecutive Interior Angles that are Interior

and on the same side of the transversal

?3 and ?5 are Consecutive Interior

?4 and ?6 are Consecutive Interior

Example

- For each pair of angles listed
- Find the transversal that forms them
- Determine whether they are
- Alternate Interior
- Consecutive Interior
- Alternate Exterior
- Corresponding

?9 and ?6

Transversal l

Both inside, and on the same side of

transversal Consecutive Interior

Transversal j

?1 and ?12

One inside, one out. Both on the left and top of

the transversal Corresponding

Transversal j

?10 and ?1

Both outside, on opposite sides of the

transversal Alternate Exterior

Assignment

- HW Pg 128, 22-32 evens

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