hand with pencil
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 ?

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

SolutionLet’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 is perpendicular to segment PQ at point R, and PRRQ, how many points on line m are equidistant from point and point ?

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 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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