GMAT Math : Geometry
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Example Questions
Example Question #1 : Understanding Intersecting Lines
Which of the following is not a valid name for the triangle in the above diagram?
All of the names in the other four choices are valid names for the triangle.
All of the names in the other four choices are valid names for the triangle.
A triangle can be named after its three vertices in any order. Since the vertices of the triangle are 
Example Question #2 : Understanding Intersecting Lines
Refer to the above diagram.
Which of the following is not a valid alternative name for 
An angle can be given a name with three letters if the middle letter is the name of the vertex and the other two letters denote points on different sides of the angle. All four of the three-letter choices fit this description.
An angle can be given a one-letter name if the letter is the name of the vertex and if it is the only angle shown in the diagram to have that vertex (thereby avoiding ambiguity). There are four angles in the diagram with vertex 
Example Question #3 : Understanding Intersecting Lines
There is no angle that forms a linear pair with 
Two angles form a linear pair if they have the same vertex, they share one side, and their interiors do not intersect. 
Example Question #4 : Understanding Intersecting Lines
Note: Figure NOT drawn to scale.
Refer to the above diagram. Which is a valid alternative name for 
A line segment is named after its two endpoints in either order; 
Example Question #5 : Understanding Intersecting Lines
There is no angle that forms a vertical pair with 
Two angles are vertical if they have the same vertex and if their sides form two pairs of opposite rays. The correct choice will have vertex 
Example Question #4 : Understanding Intersecting Lines
At what point do 
To find where two lines intersect, simply set them equal to each other and solve for 
Add 
So, 
So, the 
This makes the coordinate of our intersection 
You can check your answer by plugging in the point you calculated into both equations. Both equations will be true when 
Example Question #433 : Geometry
What is the perimeter of a hexagon?
1) Each side measures 10 cm
2) The hexagon is regular.
Statement 2 ALONE is sufficient, but Statement 1 alone is not sufficient.
BOTH statements TOGETHER are sufficient, but neither statement ALONE is sufficient.
Statements 1 and 2 TOGETHER are not sufficient.
EACH statement ALONE is sufficient.
Statement 1 ALONE is sufficient, but Statement 2 alone is not sufficient.
Statement 1 ALONE is sufficient, but Statement 2 alone is not sufficient.
The perimeter is the sum of the measures of the sidelengths.
Knowing that the hexagon is regular only tells you the six sides are congruent; without the measure of any side, this does not help you.
Knowing only that each of the six sides measures 10 cm is by itself enough to calculate the perimeter to be
The answer is that Statement 1 is sufficient, but not Statement 2.
Example Question #2 : Polygons
Note: Figure NOT drawn to scale
What is the perimeter of the above figure?
Assume all angles shown in the figure are right angles.
Not enough information is given to answer the question.
This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.
We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:
Example Question #2 : Calculating The Perimeter Of A Polygon
What is the perimeter of a rectangle with a length of 
The perimeter 
Example Question #2 : Calculating The Perimeter Of A Polygon
What is the perimeter of a right triangle with a base of 
Not enough information provided
In order to find the perimeter 
We could have also noted that 
Now that we have all three side lengths, we can calculate 
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