â€¢ Angles

â€¢ Polygons (triangles, squares, etc)

â€¢ Circles

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â€¢ Coordinate geometryOn this page you can view examples of these types of questions, and also login to our advanced on-line practice software to practice free geometry questions.

**Here is an example of a geometry question from the quantitative section of the GMAT:**

In the x,y coordinate system, what is the area of a triangle with vertices A(6,0), B(0,3) and C(8,10)?

â€¢ 31.5

â€¢ 33

â€¢ 38

â€¢ 41.5

â€¢ 42

**Solution:**

We are being asked about the area of the triangle and we are given its vertices’ locations. If we draw it, it will look like this:

We can calculate the area of the triangle by multiplying the base by the height and then dividing by 2. In principle, we can calculate the area of triangle ABC by finding out the distance between two of the coordinates and finding the corresponding height. But this lengthy process contains many calculations, will take time and is susceptible to mistakes.

There is a much simpler way to calculate the area of this triangle.Â A rectangle, which is comprised of triangle ABC and three other triangles which are right angled, can be created as shown in the figure below.Â The areas of the three right angled triangles can be easily found and then subtracted from the area of the rectangle in order to give us the area of triangle ABC.

The area of the rectangle is 8 multiplied by 10 which is 80:

The area of the right angled triangles is:

1. 3Ã—6Ã·2=9

2. 2Ã—10Ã·2=10

3. 7Ã—8Ã·2=28

That is to say, the total of the three right angled triangles is 9+10+28=47, and the area of triangle ABC is 80-47=33

**Here is another example of a geometry question from the quantitative section of the GMAT, this time in the form of a Data Sufficiency question:Â **

(Click here to read more about the DS format):

In the right triangle ABC, is angle ABC equal to angle BCA?

(1) Angle ABC = 45ÌŠ

(2) ABC is an isosceles triangle

(A)Â Â Statement (1) ALONE is sufficient to answer the question, but statement (2) ALONE is not.

(B)Â Â Â Statement (2) ALONE is sufficient to answer the question, but statement (1) ALONE is not.

(C)Â Â Â Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement alone is sufficient.

(D)Â Â Either statement by itself is sufficient to answer the question.

(E)Â Â Â Statements (1) and (2) taken together are not sufficient to answer the question, and additional data are needed to answer the question.

**Solution:**

We are told that triangle ABC is a right angled triangle and we are asked if the angles ABC and BCA are equal.

The first statement informs us that angle ABC equals 45 degrees. The problem is that we still don’t know if angle BCA is equal to 45 degrees or 90 degrees. That means that this statement isn’t sufficient to answer the question.

The second statement tells us that triangle ABC is an isosceles triangle. From this we understand that two angles equal 45 degrees and another angle equals 90 degrees. However, we still don’t know if the angles ABC and BCA are both equal to 45 degrees or if one is equal to 90 degrees. Therefore, this data isn’t sufficient to answer the question.

When we take both statements into account together, we still cannot know whether both these angles are equal to 45 degrees or if one is equal to 90 degrees. Therefore, both statements are insufficient to answer the question.

And so the answer is E.

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