On the toolbar above, click on the mouse arrow and select the Pen. Draw tick marks on the parallel line segments to indicate which sides are parallel.

On the toolbar above, click on red triangle and choose "Polygon". Choose one of the two triangles we are going to prove are congruent and shade it in. You can do this by clicking on all three vertices and then again on the point you started with (4 clicks total). Do the two triangles look congruent?

When we have parallel lines, we usually can find congruent angles somewhere. By either using the properties of parallel lines or by just looking at the size of the angles, what angles do you think are congruent? You can either type out the angles below or identify them above using the Pen tool.

Let's test our predictions for congruent angles. On the toolbar, click the angle with the red arc and the [math]\alpha[/math] next to it. Select the option "Angle". Find the measure of [math]\angle ABC[/math] by clicking the points A,B,C in that order. What is the measure of that angle?

Now find the measures of [math]\angle BCA[/math] ,[math]\angle DCB[/math], and [math]\angle CBD[/math] by using the Angle tool and clicking the points in the order of each angle listed in this question. If you get a really large angle click the undo button and reverse the order you clicked them.[br][br]Do you see two pairs of congruent angles? Were they the ones you predicted?

What property of parallel lines and transversals did we just use?

In order to use Angle-Side-Angle, we need a side length that is congruent [i]between[/i] our congruent angles. Is there such a side? If so, what side is it?

What do we call the property where if two triangles share the same side then that side must be congruent to itself?

Are the two triangles congruent? How do you know? [br]