Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
Triangles are everywhere on the GMAT. Even in problems where you do not see any gmat triangles, there are often ways to draw triangles in the diagram that aide you in solving the problem. It is paramount that you understand all of these rules and can comfortably move between them.
There are three types of triangles that will be prevalent on the exam:
Isosceles Triangle: A triangle that has two sides that are of equal length and two angles of equal measure (these are opposite the sides of equal length).
Equilateral Triangle: A triangle that has all three sides of equal length and all three angles of equal measure.
Right Triangle: A triangle that has one angle equal to 90° .
You can also have an isosceles right triangle in which there is a 90° angle and the two legs are equal to each other. This will be discussed in detail when we tackle right triangles.
An important point when discussing triangles is that the sum of the interior angles always equals 180° .
In the example of an equilateral triangle, all of the angles will measure 60° .
The diagrams on the previous page show the measure of angles within an equilateral triangle. The diagram on the right demonstrates what happens when the altitude (or height) of an equilateral triangle is drawn. The key point here is that a 30-60-90 triangle is drawn. We will go into detail with this in the discussion on right triangles, but remember that such a triangle is created.
Altitude: The perpendicular distance from the base to the opposite vertex.
Base: Any side of a triangle.
Vertex: Any angle in a triangle.
When looking at isosceles triangles, remember that the angles opposite the two equal sides are equal in measure.
In the above example AB = CD . Thus, the two opposite angles are equal. A key point is that if you have the isosceles triangle above, you only need to know the measure of angle B or A to be able to calculate each of the angles.
There are two calculations that you may have to perform when looking at triangles (or other two-dimensional geometric figures): 1) the area and 2) the perimeter.
Perimeter: The sum of all of the lengths of the sides of figure.
Area of a triangle: .5(base)(height ) or .5bh.
Another thing that the GMAT loves to cover is similar triangles. Finding similar is often key to finding a piece of information that will unlock the problem that you are trying to solve. If you have similar triangles, then the ratios of the sides of the similar triangles are the same. The way the GMAT will be able to figure out that triangles are similar is if all of the angles of one triangle are identical to the angles of another triangle. There are other ways to figure this out, but they will not be tested.
Similar Triangles: Triangles that have the same shape. This is determined by having 3 sets of congruent (of the same measure) angles.
As the triangles above are similar, it means the ratios of corresponding sides are all equal or:
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