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Published in: Full Name Comment goes here. Are you sure you want to Yes No. But fortunately I didn't, thanks to Jeevan's guide! When I read it, I found out exactly where I was going wrong all this time! I was shocked and I thought it was a total fluke so I put his strategy to the test again.

If only I came across Jeevan's strategy sooner. Learn more.. Browse by Genre Available eBooks Show More. Keep in mind that the altitude divides the triangle into two little right triangles, so the Pythagorean Theorem below may be involved in finding some of the necessary lengths.

The sum of any two sides is greater than the third. If one side is 3 and one side is 5, call the third side x.

Remember that numbers are not necessarily integers on the GRE. The largest side is always opposite the largest angle, and the smallest side is always opposite the smallest angle.

In this diagram, PQ is clearly the shortest side, so angle R has to be the smallest angle. Similarly, PR is longest side, so angle Q must be the largest angle. Geometry Rules: Isosceles Triangles One geometry rule related to this last fact concerns one elite category of triangles: the isosceles triangles.

These are triangles with two equal sides. In fact, Mr. Euclid pointed out that this geometry rule works both ways: if we are told two sides are equal, then we know two angles are equal, and if we are told two angles are equal, we know two sides are equal.

Super-technically, an isosceles triangle is one that has at least two equal sides. This means that a very special case of isosceles is the equilateral triangle. This is the most symmetrical triangle.

Be careful not to assume that a triangle is equilateral: you cannot assume one is equilateral just because it appears as one. Geometry Rules: Right Triangles Any right triangle has two sides touching the right angle: these are called legs.

The longest side, always opposite the right angle, is called the hypotenuse.

One geometry rule that applies to all right triangles is theorem named for Mr. Pythagoras — BCE , whom some scholars consider the first mathematician. Also, notice that we can apply this formula unless we know a triangle is a right triangle, and that is not something we can assume simply from looks. Of course, some or all of the sides of a right triangle can be decimals, but it is possible, in special cases, for all three sides to be integers.

These are sets of three integers that satisfy the Pythagorean Theorem. There are two very special triangles that you have to understand for GRE geometry.

The first is the triangle: We can multiply these lengths by any multiple, but they are always in this ratio. The longer leg is always the square root of 3 times longer than the shorter leg. The ratios and angles in this triangle come direction from an equilateral triangle that was cut in half: for a detailed discussion of this view, see this GMAT post.

The other triangle is the triangle, also known as the Isosceles Right Triangle. Again, the ratios always are the same and we can multiply by any number. The two legs are always equal because this is an isosceles triangle, and the hypotenuse is always the square-root of two times any leg.

GRE loves all the geometry formulas associated with these two triangles. This number, pi, can be approximated by the decimal 3. The distance from the center out to the circle in any direction is called the radius r. The second is just a restatement of the definition of pi, given above.