Counting Perpendicular Lines: Geometric Diagram Analysis

Remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

We will draw straight lines from each of the marked points in the figure to examine whether the angles are right angles.

The drawing will look like this:

Notice that from the drawing, angle BAD is greater than 90 degrees while angle CDA is less than 90 degrees.

The right angles in the drawing are:

$ABC,DCB$

The lines that form angle ABC are: AB+BC

The lines that form angle DCB are: DC+CB

Notice that if we draw angle BAD and angle CDA, we can see that these angles are greater than 90 degrees, and therefore the lines that form them are not perpendicular.

Given that there are 2 angles of 90 degrees marked in the drawing, we must have 2 pairs of perpendicular lines.