Relationship of Angles on Two Parallel Lines Intersected by Another Line

Drawing and Animating Angle Relationships on Two Parallel Lines

This article explains how to draw and animate angle relationships on two parallel lines intersected by another line using GeoGebra. This topic is commonly studied in grade VII mathematics.

Drawing Angles on Two Parallel Lines

The following steps show how to draw two parallel lines, a transversal, and the related angles.

Steps 1-3: Creating Parallel Lines

1. Open GeoGebra.
2. Draw a line through points A and B. Click Line, then create points such as A (-6, 5) and B (2, 5).
3. Click Parallel Line, then click line AB. Place the new parallel line through point C (-3, 2).

Steps 4-5: Creating the Transversal and Points

4. Draw a line passing through points A and C so that it intersects both parallel lines.
5. Add points on the lines, for example D, E, F, G, H, and I. These points are used to measure angles and observe their relationships.

Steps 6-7: Creating and Tidying the Angles

6. Click Angle and create the angles DAE, EAF, FAC, CAD, HCA, ACG, GCI, and ICH.
7. Tidy the figure by giving equal angles the same color.

Creating Animations of Angle Relationships

After the base figure is ready, create animations for several angle pairs.

Animation of Corresponding Angles

1. Click Slider, then choose Check Box.
2. Click on the coordinate plane to place the Check Box.
3. Fill the Caption field with Corresponding angles pair 1.
4. Click the small arrow below Caption, then choose Angle between D,A,E and Angle between H,C,A. Click OK.
5. When the check mark is clicked, the corresponding angles disappear. Click the Check Box again to show them.
6. Repeat the same steps for the other corresponding pairs: $\angle EAF$ and $\angle ACG$, $\angle FAC$ and $\angle GCI$, and $\angle CAD$ and $\angle ICH$.

Try the animation below.

Animation of Alternate Interior and Alternate Exterior Angles

1. Click Slider, then choose Check Box.
2. Click on the coordinate plane to place the Check Box.
3. Fill the Caption field with Alternate interior angles pair 1.
4. Select Angle between F,A,C and Angle between H,C,A.
5. Another alternate interior pair is $\angle DAC$ and $\angle ACG$.
6. Fill the Caption field with Alternate exterior angles pair 1.
7. Select Angle between D,A,E and Angle between G,C,I.
8. Another alternate exterior pair is $\angle EAF$ and $\angle HCI$.

Try the animation below.

Animation of Same-Side Interior and Same-Side Exterior Angles

1. Click Slider, then choose Check Box.
2. Click on the coordinate plane to place the Check Box.
3. Fill the Caption field with Same-side interior angles pair 1.
4. Select Angle between D,A,C and Angle between H,C,A.
5. Another same-side interior pair is $\angle FAC$ and $\angle ACG$.
6. Fill the Caption field with Same-side exterior angles pair 1.
7. Select Angle between D,A,E and Angle between I,C,H.
8. Another same-side exterior pair is $\angle EAF$ and $\angle GCI$.

Try the animation below.

Closing

That concludes this guide to drawing and animating angle relationships on two parallel lines intersected by another line in GeoGebra. If you have suggestions or corrections, please leave them in the comments or contact me here. More GeoGebra animation examples can also be found on this website.