Geometry, Section 3-1: Parallel Lines and Transversals

Geometry,

Section 3-1

Parallel Lines and Transversals

Objectives

• Students will be able to identify the relationship between two lines or two planes.

• Students will be able to name angles formed by a pair of lines and a transversal.

• G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line, and distance around a circular arc.

Angle Relations

• Please copy the diagram on the right.

• You will be given a name of an ANGLE RELATIONSHIP.

• Consider the meaning of the name of the ANGLE RELATIONSHIP.

• Try to determine what angles fit the ANGLE RELATIONSHIP.

Open Ended

What do you think "Interior Angles" might mean?

Multiple Choice

Which angles do you think are "Interior Angles"?

• 
  

  $\angle1,\ \angle2,\ \angle3\ and\ \angle4$
  

• $\angle5,\ \angle6,\ \angle7\ and\ \angle8$

• $\angle1,\ \angle3,\ \angle6\ and\ \angle8$

• $\angle2,\ \angle4,\ \angle5\ and\ \angle7$

Interior Angles

The interior angles are all the angles between the two lines which are cut by the transversal.

The INTERIOR ANGLES are:

 $\angle2$ ,  $\angle4$ ,  $\angle5$ and  $\angle7$  

Open Ended

What do you think EXTERIOR ANGLES might mean?

Multiple Choice

Which angles do you think are "Exterior Angles"?

• 
  

  $\angle1,\ \angle2,\ \angle3\ and\ \angle4$
  

• $\angle5,\ \angle6,\ \angle7\ and\ \angle8$

• $\angle1,\ \angle3,\ \angle6\ and\ \angle8$

• $\angle2,\ \angle4,\ \angle5\ and\ \angle7$

Exterior Angles

The Exterior Angles are all those which are on the outside of the two lines which are cut by the transversal.

The EXTERIOR ANGLES are:

 $\angle1$ ,  $\angle3$ ,  $\angle6$ and  $\angle8$  

Open Ended

Now that we have discussed Interior Angles, what might it mean to be ALTERNATE INTERIOR ANGLES?

Multiple Select

Which angles do you think are "Alternate Interior Angles"?

• 
  

   $\angle2\ and\ \angle7$ 
  

•  $\angle4\ and\ \angle5$ 

•  $\angle2\ and\ \angle4$ 

•  $\angle5\ and\ \angle7$ 

•  $\angle1\ and\ \angle8$  

Alternate Interior Angles

Alternate Interior Angles are two non-adjacent interior angles on different sides of the transversal.

The pairs of ALTERNATE INTERIOR ANGLES are:

 $\angle2\ and\ \angle7$ 
and 
 $\angle4\ and\ \angle5$  

Open Ended

Now that we have discussed Interior Angles (and Alternate Interior Angles), what might it mean to be CONSECUTIVE INTERIOR ANGLES?

Multiple Select

Which angles do you think are "Consecutive Interior Angles"?

• 
  

   $\angle2\ and\ \angle5$ 
  

•  $\angle4\ and\ \angle7$ 

•  $\angle2\ and\ \angle4$ 

•  $\angle5\ and\ \angle7$ 

•  $\angle1\ and\ \angle6$  

Consecutive Interior Angles

Consecutive Interior Angles are two non-adjacent interior angles on the same side of the transversal.

The pairs of CONSECUTIVE INTERIOR ANGLES are:

 $\angle2\ and\ \angle5$  
and 
 $\angle4\ and\ \angle7$  

Open Ended

We have discussed Exterior Angles, what might it mean to be ALTERNATE EXTERIOR ANGLES?

Multiple Select

Which angles do you think are "Alternate Exterior Angles"?

• 
  

   $\angle1\ and\ \angle8$ 
  

•  $\angle3\ and\ \angle6$ 

•  $\angle1\ and\ \angle6$ 

•  $\angle3\ and\ \angle8$ 

•  $\angle6\ and\ \angle8$  

Alternate Exterior Angles

Alternate Exterior Angles are two non-adjacent exterior angles on different sides of the transversal.

The pairs of ALTERNATE EXTERIOR ANGLES are:

 $\angle1\ and\ \angle8$ 
and 
 $\angle3\ and\ \angle6$  

Open Ended

"Consecutive Exterior Angles" DO NOT exist!

Why do you thing that is?

Open Ended

What might it mean to be CORRESPONDING ANGLES?

Multiple Select

Which angles do you think are "Corresponding Angles"?  (Check all that apply.)

• 
  

   $\angle1\ and\ \angle5$ 
  

•  $\angle2\ and\ \angle6$ 

•  $\angle3\ and\ \angle7$ 

•  $\angle4\ and\ \angle8$ 

•  $\angle3\ and\ \angle8$  

Corresponding Angles

Corresponding Angles are one interior and one exterior angles on the same side of the transversal.

The pairs of CORRESPONDING ANGLES are:

 $\angle1\ and\ \angle5$ ,  $\angle2\ and\ \angle6$ ,
 $\angle3\ and\ \angle7$ , and  $\angle4\ and\ \angle8$