Draw Your Own Figure

Today I would like to remind you of a very simple but effective strategy for solving math problems on standardized tests such as the ACT, SAT, and GRE.

If a math problem does not have a figure above it, then do not hesitate to draw your own. Sometimes drawing a quick picture of a situation makes a problem very easy, or at least easier. This is especially helpful with geometry problems.

Example: Segment PQ has midpoint M. If the length of PM is t, what is the length of PQ in terms of t ?

Try to solve the problem yourself before checking the solution below.

Solution: Let’s begin by drawing a picture

From the picture, we see that PQ has twice the length of PM. Thus, the length of PQ is 2t.

Here are a few more problems for you to try. Try to draw a picture. I will provide solutions to these over the next few days.

1. What is the area of a right triangle whose sides have lengths 14, 48, and 50?

2. If line m is perpendicular to segment PQ at point R, and PR = RQ, how many points on line m are equidistant from point P and point Q ?

A) One
B) Two
C) Three
D) More than three

3. Point A is a vertex of a 6-sided polygon. The polygon has 6 sides of equal length and 6 angles of equal measure. When all possible diagonals are drawn from point A in the polygon, how many triangles are formed?

4. In rectangle PQRS, point T is the midpoint of side PQ. If the area of quadrilateral QRST is 0.8, what is the area of rectangle PQRS ?

More Problems with Explanations

If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.

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