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423 Terms
Point
An exact location with no size.
Line
A straight path extending forever in both directions.
Line Segment
Part of a line with two endpoints.
Ray
Part of a line with one endpoint extending forever in one direction.
Parallel Lines
Lines that never intersect and have the same slope.
Perpendicular Lines
Lines that intersect at a ninety degree angle.
Acute Angle
An angle measuring less than ninety degrees.
Right Angle
An angle measuring exactly ninety degrees.
Obtuse Angle
An angle measuring greater than ninety degrees but less than one hundred eighty degrees.
Straight Angle
An angle measuring one hundred eighty degrees.
Vertical Angles
Opposite angles formed by intersecting lines. They are always congruent.
Adjacent Angles
Angles sharing a common side and vertex.
Complementary Angles
Two angles whose measures add to ninety degrees.
Supplementary Angles
Two angles whose measures add to one hundred eighty degrees.
Linear Pair
Adjacent angles that form a straight line and are supplementary.
Corresponding Angles
Angles in matching positions formed by a transversal crossing parallel lines. They are congruent.
Alternate Interior Angles
Angles inside parallel lines on opposite sides of a transversal. They are congruent.
Alternate Exterior Angles
Angles outside parallel lines on opposite sides of a transversal. They are congruent.
Same Side Interior Angles
Interior angles on the same side of a transversal. They are supplementary.
Triangle
A polygon with three sides.
Sum of Interior Angles of a Triangle
One hundred eighty degrees.
Exterior Angle of a Triangle
Equals the sum of the two remote interior angles.
Acute Triangle
All angles are less than ninety degrees.
Right Triangle
Contains one ninety degree angle.
Obtuse Triangle
Has one angle greater than ninety degrees.
Isosceles Triangle
Has at least two congruent sides and two congruent base angles.
Equilateral Triangle
Has three congruent sides and three sixty degree angles.
Scalene Triangle
Has no congruent sides.
Pythagorean Theorem
a squared plus b squared equals c squared where c is the hypotenuse.
Pythagorean Triple
Common triples include three four five five twelve thirteen and eight fifteen seventeen.
Hypotenuse
The side opposite the right angle and the longest side of a right triangle.
Leg
One of the two shorter sides of a right triangle.
Distance Formula
The square root of quantity x2 minus x1 squared plus quantity y2 minus y1 squared.
Midpoint Formula
Quantity x1 plus x2 divided by two comma quantity y1 plus y2 divided by two.
Slope Between Two Points
Quantity y2 minus y1 divided by quantity x2 minus x1.
Triangle Area Formula
One half times base times height.
Herons Formula
Square root of quantity s times quantity s minus a end quantity times quantity s minus b end quantity times quantity s minus c end quantity where s equals half the perimeter.
Similar Figures
Figures with equal corresponding angles and proportional corresponding sides.
Congruent Figures
Figures with the same size and shape.
Similarity Ratio
The ratio of corresponding side lengths in similar figures.
Scale Factor
The multiplier relating corresponding lengths of similar figures.
Perimeter
The sum of the side lengths of a figure.
Circumference Formula
Two times pi times radius or pi times diameter.
Circle
The set of all points the same distance from a center.
Radius
The distance from the center of a circle to its edge.
Diameter
Twice the radius.
Chord
A segment with both endpoints on a circle.
Tangent
A line touching a circle at exactly one point.
Secant
A line intersecting a circle at two points.
Arc
A portion of a circle.
Central Angle
An angle whose vertex is at the center of the circle.
Inscribed Angle
An angle whose vertex lies on the circle. Its measure is half the intercepted arc.
Arc Length Formula
Quantity central angle divided by three hundred sixty end quantity times two pi radius or radius times angle in radians.
Sector Area Formula
Quantity central angle divided by three hundred sixty end quantity times pi radius squared or one half radius squared times angle in radians.
Area of a Circle
Pi times radius squared.
Equation of a Circle
Quantity x minus h end quantity squared plus quantity y minus k end quantity squared equals radius squared.
Rectangle Area
Length times width.
Rectangle Perimeter
Two times quantity length plus width.
Square Area
Side squared.
Square Perimeter
Four times side.
Parallelogram Area
Base times height.
Rhombus Area
One half times diagonal one times diagonal two.
Trapezoid Area
One half times quantity base one plus base two end quantity times height.
Kite Area
One half times diagonal one times diagonal two.
Regular Polygon
A polygon with all sides and all angles congruent.
Interior Angle Sum Formula
Quantity number of sides minus two end quantity times one hundred eighty.
Each Interior Angle of a Regular Polygon
Quantity number of sides minus two end quantity times one hundred eighty divided by number of sides.
Exterior Angle Sum of Any Polygon
Three hundred sixty degrees.
Each Exterior Angle of a Regular Polygon
Three hundred sixty divided by number of sides.
Cube Volume
Side cubed.
Cube Surface Area
Six times side squared.
Rectangular Prism Volume
Length times width times height.
Rectangular Prism Surface Area
Two quantity length width plus length height plus width height end quantity.
Cylinder Volume
Pi radius squared height.
Cylinder Surface Area
Two pi radius squared plus two pi radius height.
Cone Volume
One third pi radius squared height.
Sphere Volume
Four thirds pi radius cubed.
Sphere Surface Area
Four pi radius squared.
Right Circular Cone
A cone with its vertex directly above the center of the base.
SOHCAHTOA
Sine equals opposite divided by hypotenuse cosine equals adjacent divided by hypotenuse tangent equals opposite divided by adjacent.
Sine Function
Opposite divided by hypotenuse.
Cosine Function
Adjacent divided by hypotenuse.
Tangent Function
Opposite divided by adjacent.
Reciprocal Identities
Cosecant equals one divided by sine secant equals one divided by cosine cotangent equals one divided by tangent.
Pythagorean Identity
Sine squared plus cosine squared equals one.
Thirty Sixty Ninety Triangle
Side ratio one square root three two.
Forty Five Forty Five Ninety Triangle
Side ratio one one square root two.
Radian Measure
Pi radians equals one hundred eighty degrees.
Degree to Radian Conversion
Multiply degrees by pi divided by one hundred eighty.
Radian to Degree Conversion
Multiply radians by one hundred eighty divided by pi.
Unit Circle
A circle with radius one centered at the origin used to determine exact trig values.
Sine of Zero
Zero.
Cosine of Zero
One.
Sine of Thirty
One half.
Cosine of Thirty
Square root three divided by two.
Sine of Forty Five
Square root two divided by two.
Cosine of Forty Five
Square root two divided by two.
Sine of Sixty
Square root three divided by two.
Cosine of Sixty
One half.
Sine of Ninety
One.