GRE Math: How to solve Special Triangles on GRE ? {Simple Approach}

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GRE Math: How to solve Special Triangles on GRE ? {Simple Approach}

While geometry questions on the GRE use a variety of shapes and figures, knowing the properties of the most commonly tested figures prepares you to answer just about any geometry question you'll encounter. For example, the sum of the angle measures in a triangle is always 180 degrees. Special triangles are one of the most important categories of figures to master, since nearly every figure that isn't round will include one or more special triangles that you can use to your advantage.

For instance, knowing the length of one side of a 30°-ó0°-90° triangle or 45°-45°-90° triangle enables you to find the lengths of the other sides. In some cases, you can use this knowledge to uncover more information about the original figure.

For example

In the triangle above, what is the length of side BC?

A) 4

B) 5

C) 4√2

D) 6

E) 5√2

If you think the 45° angle might turn out to be useful, you are correct. But don't jump to any conclusion yet! The triangle may look like a right isosceles triangle (a 45°-45°-90° triangle), but remember, you can't always trust your first impression of diagrams on the GRE. Use the information explicitly given in the question stem and the figure instead.

The special triangles you should look for on the GRE are summarized below. Read about

those triangles, and then you will be ready to return to the problem above

You can draw a line segment from point B, perpendicular to side AC. This divides the triangle into two right triangles.

The triangle on the left has a 45° angle and a 90° angle. Since the Jum of the angle measures in any triangle is 180°, the third angle is 45°. So the triangle is a 45°-45°-90° triangle.

The hypotenuse is 4√2, so the side lengths form the ratio 4:4:4√2, which is equivalent to 1:1:√2