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GMAT Math Review > Geometry > Flashcards

Flashcards in Geometry Deck (23):


a. Refers to a straight line that extends without end in both directions.


Line segment

a. The part of the line denoted by XY


Intersecting lines and angles

a. If two lines intersect, the opposite angles are called vertical angles and have the same measure.


Perpendicular lines

a. If two lines intersect at right angles, the lines are perpendicular.


Parallel lines

a. If two lines that are in the same plane do not intersect, the two lines are parallel.
b. If two lines are intersected by a third lined then vertical angles are created that are equal on both lines.


Define polygon

a. A closed plane figure formed by three or more line segments, called the sides.
b. Each side intersects exactly two other sides at their endpoints, the points of intersection are called verticies.
c. Convex polygon, each interior angle has a measure of less than 180 degrees.


Universal summation rule ( Triangle )

a. The sum of the length of any two sides is greater than the remaining side.


Equilateral triangle

a. Has all sides of equal length. All angles are of equal measure.


Isosceles triangle

a. Has at least two sides of the same length. If two sides of a triangle have the same length then the two angles have the same measure.


Pythagorean theorem

a. The square of the length of the hypotenuse is equal to the sum of the squares of the legs. ( Right Triangles )


Right triangles

a. Any triangle in which the lengths of the sides are in the ratio 3:4:5
b. a^2 + b^2 = c^2


45 – 45 – 90 Triangle

a. The length of the sides are in the ratio 1:1: Square root of 2


30 – 60 – 90 Triangle

a. The lengths of the sides are in the ratio 1:Square root of 3:2


Area of a triangle

a. If not an equilateral triangle then ½ * b * h



a. A quadrilateral in which both pairs of opposite sides are parallel. The opposite sides also have equal length.
b. The diagonals bisect each other such that each side of single diagonal equals the other side.
c. The area is equal to the length of the altitude * the length of the base.



a. A parallelogram with right angles is a rectangle, and a rectangle with all sides of equal length is a square.
b. The diagonals are equal and apart of a right triangle.



a. Only two sides are parallel
b. Area is calculated; ½ * (sum of bases)(height)



a. Is a set of points in a plane that are all located the same distance from a fixed point (the center of the circle).
b. A chord of a circle is a line segment that has its endpoints on the circle. A chord that passes through the center is a diameter.
c. A radius is a segment from the center of the circle to a point on the circle.



a. Is the distance around a circle.
b. 2 * pie * r


Area of a Circle

a. Pie * r^2


Arc in a circle

a. In a complete rotation = 360 degrees
b. The length of an arc is equal to x / 360 * the circumference of the circle where x is equal to the angle within the arc.


Tangent to a circle

a. A line that has exactly one point in common with a circle is said to be tangent to the circle.
b. A radius or diameter with an endpoint at the point of tangency is perpendicular to the tangent line. ( therefore there is a right angle ).


Triangles and circles

a. If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle, the triangle is a right triangle.