In this activity, you will use an interactive dynamic geometry sketch to investigate the relationships between the measures of corresponding angles, alternate interior angles, and alternate exterior angles. Click on this link to open the following exercise and follow the instructions below:

Interactive Transversal Angles

Before starting click on Unlock lines and Toggle Grid.

1. Click on Alternate Interior. They will be highlighted on the graph. Move both the parallel lines and the transversal.
2. Observe the angles and their measurements.
3. Click on Alternate Exterior. They will be highlighted on the graph. Move both the parallel lines and the transversal.
4. Observe the angles and their measurements.
5. Click on Corresponding. They will be highlighted on the graph. Move both the parallel lines and the transversal.
6. Observe the angles and their measurements.

Respond to the questions below in your notes.

1. If two lines are parallel and are cut by a third line, called a transversal, what is the relationship between the following pairs of angles? Click the links below to check your answers.



Interactive popup. Assistance may be required. Corresponding Angles They are congruent.


Interactive popup. Assistance may be required. Alternate Interior Angles They are congruent.


Interactive popup. Assistance may be required. Alternate Exterior Angles They are congruent.


2. Is the relationship for parallel lines also true when the lines are not parallel? Why or why not?

   Interactive popup. Assistance may be required. Check Your Answer Notice that the congruent relationships are not true when the lines are not parallel.
   

Now, let's investigate two more angle relationships in parallel lines. Open the following exercise and follow the instructions below:

Interior Angles of a Transversal

1. Drag the orange dot for point A or point B. Observe what happens.
2. Now, drag the orange dot for point P. Observe what happens.
3. Return to Epsilen when you have completed your investigation.

Source: Math Open Reference – Interior Angles of a Transversal

Two angles that are in the interior region between two parallel lines and on the same side of the transversal are called... Interactive popup. Assistance may be required. Check Your Answer same-side interior angles or consecutive interior angles

Respond to the questions below. Click the links below to check your answers.

1. What did you notice as you dragged point A or point B around the sketch? What does this tell you about the relationship between consecutive interior angles?

   Interactive popup. Assistance may be required. Check Your Answer Observe that the consecutive interior angles are supplementary; that is, the sum of their measures always equals 180°.
   

2. Is this relationship true when the lines are not parallel? Why or why not?

   Interactive popup. Assistance may be required. Check Your Answer Observe that the relationship does not hold true when the lines are not parallel.
   

To investigate the last pair of special angles, open the following exercise and follow the instructions below:

Exterior Angles of a Transversal

1. Drag the orange dot for point A or point B. Observe what happens.
2. Now, drag the orange dot for point P. Observe what happens.
3. Return to Epsilen when you have completed your investigation.

Source: Math Open Reference - Exterior Angles of a Transversal

Two angles that are in the exterior region outside of two parallel lines and on the same side of the transversal are called... Interactive popup. Assistance may be required. Check Your Answer same-side exterior angles or consecutive exterior angles

Respond to the questions below. Click the links below to check your answers.

1. What did you notice as you dragged point A or point B around the sketch? What does this tell you about the relationship between consecutive exterior angles?

   Interactive popup. Assistance may be required. Check Your Answer Observe that the consecutive exterior angles are supplementary; that is, the sum of their measures always equals 180°.

2. Is this relationship true when the lines are not parallel? Why or why not?

   Interactive popup. Assistance may be required. Check Your Answer Observe that the relationship does not hold true when the lines are not parallel.