Gmat Math (Geometry)

Front 1

line

Back 1

refers to a straight line that extends without end in both directions

Front 2

line segment

Back 2

_P________________Q_
P and Q are the endpoints of the segment

Front 3

polygon

Back 3

a closed plane figure formed by three or more line segments, called the sides of the polygon. Each side intersects exactly two other sides at their endpoints. The points of intersection of the sides are vertices. The term “polygon” will be used to mean a convex polygon, that is, a polygon in which each interior angle has a measure of less than 180°.A polygon with three sides is a triangle; with four sides, a quadrilateral; with five sides, a pentagon; and with six sides, a hexagon.

Front 4

triangle

Back 4

There are several special types of triangles with important properties. But one property that all triangles share is that the sum of the lengths of any two of the sides is greater than the length of the third side.

Front 5

quadrilaterals

Back 5

A polygon with four sides is a quadrilateral. A quadrilateral in which both pairs of opposite sides are parallel is a parallelogram. The opposite sides of a parallelogram also have equal length.

Front 6

circles

Back 6

A circle is a set of points in a plane that are all located the same distance from a fixed point (the center of the circle). A chord of a circle is a line segment that has its endpoints on the circle. A chord that passes through the center of the circle is a diameter of the circle. A radius of a circle is a segment from the center of the circle to a point on the circle. The words “diameter” and “radius” are also used to refer to the lengths of these segments.

Front 7

rectangular solid

Back 7

a three-dimensional figure formed by six rectangular surfaces, as shown below. Each rectangular surface is a face. Each solid or dotted line segment is an edge, and each point at which the edges meet is a vertex. A rectangular solid has six faces, twelve edges, and eight vertices. Opposite faces are parallel rectangles that have the same dimensions. A rectangular solid in which all edges are of equal length is a cube.

Front 8

coordinate plane

Back 8

x and y axis; The horizontal line is called the x-axis and the perpendicular vertical line is called the y-axis.
The point at which these two axes intersect, designated O, is called the origin.
The axes divide the plane into four quadrants, I, II, III, and IV- counterclockwise

Front 9

points in the coordinate plane

Back 9

Each point in the plane has an x-coordinate and a y-coordinate. A point is identified by an ordered pair (x,y) of numbers in which the x-coordinate is the first number and the y-coordinate is the second number.

Front 10

distance between two points

Back 10

One way to find the distance between two points in the coordinate plane is to use the Pythagorean theorem. a2+b2=c2

Front 11

lines in the coordinate plane

Back 11

For a line in the coordinate plane, the coordinates of each point on the line satisfy a linear equation of the form y = mx + b (or the form x = a if the line is vertical).

Front 12

slope of a line

Back 12

In the equation of a line y = mx + b, the coefficient m is the slope of the line and the constant term b is the y-intercept of the line. For any two points on the line, the slope is defined to be the ratio of the difference in the y-coordinates to the difference in the x-coordinates.

Front 13

x- and y-intercepts of a line

Back 13

The y-intercept is the y-coordinate of the point at which the line intersects the y-axis. The x-intercept is the x-coordinate of the point at which the line intersects the x-axis. The x-intercept can be found by setting y = 0 and solving for x.

Front 14

Equation of a line given any two points

Back 14

slope- m=y2-y1/x2-x1

Front 15

Negative vs. positive slope of a line

Back 15

If the slope of a line is negative, the line slants downward from left to right; if the slope is positive, the line slants upward. If the slope is 0, the line is horizontal; the equation of such a line is of the form y = b since m = 0. For a vertical line, slope is not defined, and the equation is of the form x = a, where a is the x-intercept.

Front 16

Solutions of two linear equations using the coordinate plane

Back 16

There is a connection between graphs of lines in the coordinate plane and solutions of two linear equations with two unknowns. If two linear equations with unknowns x and y have a unique solution, the graphs of the equations are two lines that intersect in one point, which is the solution. If the equations are equivalent, they represent the same line with infinitely many points or solutions. If the equations have no solution, they represent parallel lines, which do not intersect.

Front 17

Quadratic polynomial functions and the coordinate plane

Back 17

f9x0=x2-1. Plot several points and use them to graph the function.