Friday, March 22, 2013

This figure is not drawn to scale

Both the ACT and the SAT math sections are filled with figures and diagrams.  Can you trust what you see?  That depends on the test.

On the ACT none of the figures are drawn to scale.  They make this disclaimer at the beginning of the math section.  You can still trust certain aspects of the diagram.  For example, if it shows that two line segments intersect, then they really do.  Sometimes they will give you facts about the diagram that you should assume.  However, sometimes they can be mean, and looks can be deceiving.  Here are some things you CANNOT assume about the diagram. Consider the diagram below:


Unless it is stated or you can prove it given what is stated, you CANNOT assume any of the following:

  • that segment AC is tangent to the circle 
  • that point O is the center of the circle
  • that D, O and F are collinear (in other words, angle DOF could be 179°)
  • that any angle shown is a right angle, an acute angle or an obtuse angle
  • that any segment is longer than, shorter than, or the same length as another based on how they look


For the SAT on the other hand, you should assume that every figure is drawn precisely to scale unless there is a note under the figure that says otherwise.  If the figure IS drawn to scale, you can use that information to eliminate some of the answer choices. Again considering the figure above:  If you are told that segment OB is 3 inches long and asked the length of segment EF you can eliminate any answer choice that reads 3 inches or longer, since EF is clearly shorter than OB. 


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