Math Project: Rebecca Hartung
equation of a circle
(x-h)^2+(y-k)^2=r^2
circumference of a circle
2πr
Sine
A function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse. The equation looks like sin(angle) = opposite side over the hypotenuse.
Perpendicular bisector
A line, segment, or ray that is perpendicular to the segment at the midpoint.
Median
A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of the list of numbers. ex. 12,14,16,18,20,22,24,26,28,30,32 the median out of these numbers is 22.
Regular Polygon
A polygon that is both equiangular and equilateral, meaning that all of there side are equal and all of the angles are equal. ex. looking at this picture, lets say that they sides are all equal and the angles are too.
circle
A round plane figure whose boundary consists of points equidistant from the center.
Altitude
A segment from the vertex of a triangle to the opposite side and it must be perpendicular to that segment.
radius
A straight line from the center to the circumference of a circle or sphere.
diameter
A straight line passing from side to side through the center of a circle or sphere.
Tangent
A straight or curved line that intersects a circle or arc at one point only. The equation is tan(angle)=opposite side over adjacent side.
hypotenuse leg (HL)
A theorem that says that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
Base of Isosceles triangle
A triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base.
Isosceles trianlge
A triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length and the third side is the base.
Reflexive property
A value that is equal to itself.
area of a circle
A=πr²
Equilateral Triangle
All three sides and angles are equal.
CPCTC
An abbreviation for "Corresponding Parts of Congruent Triangles are Congruent," which can be used as a justification in a proof after two triangles are proven congruent.
central angles
An angle whose vertex is the center of the circle.
minor arc
An arc of a circle whose measure is less than 180 degrees.
major arc
An arc that measures to be greater than 180 degrees.
corresponding angles
Angles that have the same position on two different parallel lines cut by a transversal.
Alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
area of a segment
Area of a sector - area of a triangle = area of a segment
vertical angles
Each of the pairs of opposite angles made by two intersecting lines.
area of a sector
Find the fraction of the circle the sector represents and multiply by the area of the circle.
Transitive property
If two quantities are congruent to the same quantity, then they are congruent to each other.
Addition property
If you add the same number to both sides of an equation it will stay the same.
Division property
If you divide both sides of an equation by a nonzero number they will stay the same.
Parallel planes
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.
Parallelogram
It is a four-sided plane rectilinear figure with opposite sides parallel.
Angle bisector
It is a line or ray that divides an angle into two congruent angles.
arc
It is a portion of the circumference of a circle.
Pythagorean Triple
It is a set of three integers that make up the sides of a right triangle. ex. The image shows the smallest possible Pythagorean triple.
Dilation
It is a transformation that makes an image that is small or larger to the original. It stretches or shrinks the original shape.
exterior angle of a triangle
It is greater than either of the measures of the remote interior angles. It is an angle outside of the triangle that forms a linear pair with an interior angle.
Orthocenter
It is one of the triangle's points of concurrency formed by the intersection of the triangle's 3 altitudes.
scale factor
It is the ratio of corresponding sides in two similar figures.
Mid segment of a trapezoid
It is the segment connecting the midpoints of the two non-parallel sides.
Included side
It is the side that links two angles together.
Similar Poylgons
Polygons whose corresponding angles are congruent and whose corresponding sides are proportional
Symmetric property
Property of equality for "a" and "b": if a=b then b=a
Same side interior angles
Same Side Interior Angles are two angles that are on the same side of the transversal and on the interior of the two lines. If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
angle of depression
The angle formed by a horizontal line and the line of sight to an object below the horizontal line.
Remote interior angles
The angles of a triangle that are not adjacent to a given exterior angle
Centroid
The point of concurrency of the medians of a triangle
Incenter
The point of concurrency of the three angle bisectors of a triangle
Multiplication property
The property states the product of a number and -1 is the opposite of the number, and any number multiplied by 1 is itself.
Legs of and Isosceles triangle
The two equal sides on the isosceles triangle are legs and the third one that connects the two is called the base.
Vertex angle of an Isosceles triangle
The vertex angle is the angles where the two legs connect, it is opposite to the base.
Base angles of and Isosceles triangle
These angles have the base on either side of them.
Legs of a right triangle
These are the two sides of the right triangle that meet in a 90 degree angle.
Adjacent arcs
They are arcs of the same circle that have exactly one point in common.
Trapezoid
This is a quadrilateral who only has one pair of parallel sides.
Hypotenuse
This is the longest side to a right triangle. It is opposite to the 90 degree angle. ex. in the picture the side that has the double line is the hypotenuse.
angle angle side (AAS)
Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
SAS similarity
Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal.
Complementary
Two angles whose sum is 90 degrees
congruent circles
Two circles that have a congruent radii.
skew lines
Two lines that do not intersect and are not parallel.
Congruent polygons
Two polygons are congruent if their corresponding sides and angles are congruent.
Side angles side (SAS)
Two triangles are congruent if they have two congruent sides with a congruent angle between them.
SSS similarity
Two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, the triangles are similar.
Subtraction Property
When both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.
Supplementary
When two angles add up to 180 degrees they are supplementary angles.
side side side (SSS)
When two triangles have corresponding sides equal in length, then the two triangles are congruent.
Rectangle
a figure with four straight sides and four right angles, whose adjacent sides are unequal.
Mid segment of a triangle
a line segment that connects the midpoints of two sides of a triangle.
Transversal
a line that intersects two or more lines.
Rhombus
a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.
Square
a plane figure with four equal straight sides and four right angles.
distributive property
a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac
Kite
a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
apothem
a segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon.
Cosine
adjacent/hypotenuse
included angle
an angle between two sides of a triangle, it can be any angle depending on what it is being used for in the proofs.
semicircle
an arc with a measure of 180 degrees, or half of the circle.
Alternate interior angles
angles between 2 lines and on opposite sides of a transversal.
AA similarity
if two angles of one triangle are congruent to two corresponding angles in another triangle, then the triangles are congruent.
Angle side angle (ASA)
if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
Substitution Property
if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.
center of dilation
in a dilation, the fixed point about which the figure is enlarged or reduced.
Isosceles trapiziod
it is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
Parallel lines
lines in the same plane that never intersect.
angle of elevation
the angle formed by a horizontal line and the line of sight to an object above the horizontal line.
arc length
the distance along an arc measured in linear units.
Geometric mean
the mean of n numbers expressed as the n-th root of their product.
center of circle
the point inside a circle that is the same distance from all the point on the circle.
Circumcenter
the point where the perpendicular bisectors of the sides of a triangle intersect
Ratio
the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Pythagorean Theorem
the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.