This section is devoted to QC questions that test your knowledge of Geometry, but don’t provide a picture. For example:
| 4 points, P, Q, R, and T lie in a plane. PQ is parallel to RT and PR = QT. |
|
| Quantity A | Quantity B |
| PQ | RT |
The basic process remains the same. First, establish what you need to know.
Both quantities contain unknown values, so you need to determine the relative size of each line segment.
Now, establish what you know. For any Word Geometry question, the first thing you need to do is draw the picture.
You want to draw a picture that is accurate, but quick. And remember, you can always redraw the figure if you run into trouble.
For this question, the easiest way to start is to draw the parallel lines:
You know that points P & Q lie on one line, and R & T lie on the other, but you don’t know their relative sizes. But you do know that PR = QT:
To start, the easiest thing to do is align the points so that they form a rectangle. Now, PR = QT. This diagram reflects all the information provided.
Now, take another look at the quantities:
| Quantity A | Quantity B |
| PQ | RT |
According to the diagram, PQ = RT. 
You’re not done. You need to try to prove (D).
Now, the final step: establish what you don’t know. Remember that diagram is only one possible way to represent the common information. Ask yourself, “What can change in this diagram?”
In the previous diagram, PQ and RT were drawn perpendicular to the two parallel lines. But the angle can change. Redraw the diagram with PR and QT slanted:
This diagram represents another possible configuration of the four points. Now how does PQ compare to RT ?
Although it may not be immediately obvious, PQ is still equal to RT. Whereas the first diagram created a rectangle, this diagram has created a parallelogram. For additional practice, prove that PQRT is a parallelogram.
It may be tempting to choose choice (C) at this stage, but be careful! The key to Word Geometry questions is to avoid making any assumptions not explicitly stated in the common information.
It is not sufficient to merely change the diagram. Ask yourself, “What can I change in the diagram to change the relative size of PQ and RT?”
Changing the angle at which segments PR and QT intersected the parallel lines was not sufficient to achieve different results. What else can change?
The two preceding diagrams share a common feature that is not required by the common information:
PR and QT are parallel.
Redraw the figure so that PR and QT are NOT parallel, but still equal:
In this version of the diagram, RT is clearly longer than PQ. The answer is (D).