Essential Geometry and Algebra Glossary
Classified in Mathematics
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Geometry
Angles
Adjacent angles - that have a common vertex and side, but no common interior points
Angle - formed by two rays with a common endpoint called the vertex
Complementary angles - whose measures add up to 90°
Congruent angles - that have the same measure
Supplementary angles - two angles whose measures add up to 180°
Vertical angles - the nonadjacent angles formed by two intersecting lines
Lines
Midpoint - the point that divides a segment into two congruent segments
Parallel lines - in a plane that never meet
Perpendicular lines - that intersect at 90° angles
Transversal - a line that intersects any two or more other lines
Triangles
Triangle Inequality Theorem - the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Triangle Sum Theorem - the angle measures of a triangle add up to 180°
Transformations
Congruent figures - that have the same size and shape
Congruence transformations- that result in an image that is the same shape and the same size as the original.
Image - the resulting figure after a translation, rotation, or reflection
Reflection - flips a figure across a line to create a mirror image
Rotation - turns a figure around a point
Three-Dimensional Figures
Circumference - the distance around the circle
Cone - a figure with a circular base
Cylinder - a three-dimensional figure with two circular, parallel, and congruent bases
Hemisphere - one of two halves of a sphere
Prism - a three- dimensional figure whose two bases are parallel congruent polygons and whose faces are parallelograms
Pyramid - a figure with one polygon base and triangular faces that meet at a point
Regular pyramid - a pyramid with a regular polygon for a base and congruent lateral faces
Sphere - A set of points in three dimensions that are a fixed distance from the center
Algebra
Expressions and Equations
Equivalent expressions - expressions that have the same value for all the values of the variables
Like term - terms that have the same variable raised to the same exponent
Literal equation - equation with two or more variables
Simplify - perform all the operations possible, including combining like terms
Term - elements of an expression that are separated by plus or minus signs
Systems of Equations
Solution of a system of equations - set of values making all equations in a system true
System of equations - system of two or more equations that contain two or more variables
Linear Equations
Linear equation - equation whose solutions fall on a straight line on the coordinate plane
Point-slope form - the equation of a line in the form of y - y1 = m (x - x1), where m is the slope and (x1, y1) is a specific point on the line
Slope - the ratio of rise to run for any two points on a line
Slope-intercept form - a linear equation written in the form y = mx + b, where m is the slope and b is the y-intercept
x-intercept - the x-coordinate of the point where the line crosses the x-axis
y-intercept - the y-coordinate of the point where the line crosses the y-axis
Variation
Constant of variation - the ratio by which two variable quantities are related
Direct variation - a relationship between two variables such that the data increase or decrease together at a constant rate
Rate of change - ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable
Rise - the difference of the y-values of two points on a line
Run - the difference in the x-values of two points on a line