Page 239 - ABCTE Study Guide_Neat

But how can we be sure it’s a square? Well, we must consider what we know about squares.

• A square is a quadrilateral, so it must have four sides.
• A square is a parallelogram, so its opposite sides must be parallel.
• A square is a rectangle, so it must have four right angles.
• A square is a rhombus, so all of its sides must be congruent.

Let’s check each of these to confirm that ABCD is a square. Clearly, it has four sides but are the opposite
sides parallel? Sides AB and CD have the same steepness, so they’re parallel. In fact, they’re also
parallel to the x-axis. Sides BC and AD also have the same steepness, so they’re parallel, as well. And
they’re parallel to the y-axis. Thus, quadrilateral ABCD is a parallelogram.

The opposite angles of a parallelogram are always congruent, so now we only need to check if
angles DABand ABC are right angles. We know that perpendicular lines form right angles, so if side AD is
perpendicular to side AB, and if side AB is perpendicular to side BC, then all of the angles must be right
angles. We can check this using a protractor to measure the angles.

Here’s a close-up of angle DAB and the protractor with which we’ll measure it.

Protractor

To measure the angle:

Find the center hole on the straight edge of the protractor. Place the hole over the vertex of the angle.

• Line up the zero on the straight edge of the protractor with one of the sides of the angle.
• Find the point where the second side of the angle intersects the curved edge of the
protractor.
• Read the number that is written on the inside scale of the protractor at the point of
intersection. This is the measure of the angle in degrees.

If the side of the angle were aligned with the left side of the straight edge of the protractor, you would have
read the measure of the angle from the outside scale.

This angle measures 90°, so it is indeed a right angle. We could repeat this process to measure
angle ABC to find out that it is a right angle, too.

Question:

What is the measure in degrees of angle JKL?