Equilateral Triangle
Triangle in which all three sides are equal
Isosceles Triangle
2 sides of a triangle are equal
Angle Bisector
A line or ray that divides a angle into two congruent angles
Altitude
Line segment through a vertex and perpendicular to a line containing the base
Perpendicular Lines
Lines that meet at a 90 degree angle
Collinear Points
Three or more points that lie on a single straight line
Scalene Triangle
Triangle with three unequal sides
Perpendicular Bisector
Line that divides a line segment into two equal parts
Parallel Lines
Two lines in a same plane that do not intersect and are equidistant
Median
Line segment joining a vertex to the midpoint of the opposing side
Vertical Angles
A pair of non-adjacent angles formed when two lines intersect
Linear Pairs
A pair of supplementary and adjacent angles
Complementary Angles
Two angles that add up to 90 degrees
Supplementary Angles
Two angles that add up to 180 degrees
Alternate Interior Angles
When two lines are crossed by another line, the pairs of angles on opposite lines of the transversal, but inside the two lines
Alternate Exterior Angles
When two lines are crossed by another line, the pairs of angles on opposite lines of the transversal, but outside the two lines
Corresponding Angles
When two lines are crossed by another line, the angles in matching corners are corresponding
Same Side Interior Angles
Two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary
Same Side Exterior Angles
When a transversal crosses two lines, each pair of these angles are outside the parallel lines and the same side of the transversal
Remote Interior Angle Theorem
Two angles that are inside the triangle and opposite from the exterior angle
Auxiliary Line
Extra line needed to complete a proof in plane geometry
Midpoint
Middle point of a line segment
Congruent Triangles
Two triangles that have the same three sides and angles
SAS
Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
SSS
Three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent
ASA
Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
AAS
Two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent
Isosceles Triangle Theorem
Two sides of a triangle are congruent, then the angles opposite those sides are congruent
Converse of the Isosceles Triangle Theorem
Two angles of a triangle are congruent , then the sides opposite to these angles are congruent
Hyp- Leg
Two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles
Properties of a Parallelogram
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect each other
Properties of a rectangle
All properties of a parallelogram, all angles are rectangles, diagonals are congruent
Properties of a Rhombus
All properties of a parallelogram, all sides are congruent, diagonals bisect the angles
Properties of a Square
Diagonals bisect each other, Diagonals bisect angles, opposite sides are parallel are equal, four angles are equal, four sides are equal, diagonals are equal
Slope Formula
y=mx+b
Midpoint Formula
(x1+x2/2,y1+y2/2)
Slope Intercept Formula
Represents the equation of a line with the slope and the y-intercept
Vertical Line Equations
Has no y-intercept and slope is undefined, used to see if an relation is a function
Horizontal Lines Equations
Straight Line on coordinate plane where all points have same y-value
Point Slope Formula
equation of a straight line, y ? y1 = m(x ? x1)
Equations for Parallel Lines
Must have same slope, y-intercept can be different
Equations for Perpendicular Lines
The slopes must be negative reciprocals, same y-intercept
Writing the equation of a Median
Use the midpoint formula, then put it in point-slope form
Writing the equation of a Altitude
find the slope, then find the equation of the perpendicular bisector
Writing the equation of a Perpendicular Bisector
Find the midpoint, then find the slope of the perpendicular bisector then put it in point-slope form
Distance Formula
Distance =�(x2?x1)2+(y2?y1)2
Proving an Isosceles Triangle
2 sides are congruent and the angles and sides opposite of them are congruent
Proving an Equilateral Triangle
Needs to have the Isosceles Triangle Theorem, each angle needs to be 60 degrees,
Proving a Scalene Triangle
Prove that all sides are not equal
Proving a Right Triangle
Needs to have at least 1 Right Angle, then you can prove the HL Theorem
Proving a Parallelogram
If one pair of opposite sides of a quadrilateral are both parallel and congruent, , if the diagonals of a quadrilateral bisect each other,
Proving a Rectangle
Needs to have four right angles, 2 pairs of opposite, equal and parallel sides
Proving a Rhombus
All sides are equal, diagonals bisect all the angles
Proving a Square
4 congruent sides, if a quadrilateral is a rectangle and rhombus it is a square
Sine
Equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse
Cosine
Equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse
Tangent
opposite/adjacent
Relationship between Sine and Cosine
The cosine of any acute angle is equal to the sine of its complement
Image
The new position of a point, a line, a line segment, or a figure after a transformation
Pre-Image
The original figure prior to a transformation
Translation
Describes a function that is moved a certain distance, all sides move in same direction and distance
Reflection
Preimage is flipped across a line of reflection to create the image, each point is same distance from another
Reflection over x-axis
reflect over y=x
Reflection over y-axis
y coordinate stays the same, the x coordinate changes
Reflection over y=x
Flips the x and the y coordinates
Reflection over y=-x
Flips x and y coordinates, but makes them negative
Reflection over x=#
Reflect over the line over or below the x-axis whatever the number is
Reflection over y=#
Reflection to the left or right of the y-axis
Reflection over the origin
x and y coordinate are negated
Rotation
Has a central point that stays fixed and everything else moves around the point
Clockwise Rotation
Moves in the direction of a clock, 90 degree rotation is 1/4 of a full rotation
Counterclockwise Rotation
Moves in the opposite direction of a clock, 90 degree rotation is 1/4 of a full rotation, but in the opposite way
Dilation
Changes the size of a figure, make figure smaller or bigger but does not change shape
Center of Dilation on the line
Maps a line containing the center of dilation to itself and every line not containing the center of dilation to a parallel line
Center of Dilation not on the line
You count how many boxes between the point and the center and do that how many times the scale factor is
Rigid Motion
The relative distance between points stays the same and the relative position of the points stays the same
Scale Factor
Number which scales, or multiplies, some quantity
Point Symmetry
The same distance from the central point, but in the opposite direction
Rotational Symmetry Formula
If you can rotate a figure around a center point by fewer than 360� and the figure appears unchanged, then the figure has rotation symmetry
Regular
When all angles are equal and all sides are equal
Similar Figures
Figures that have the same shape, but may have different sizes
Side Splitter Theorem
If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally
Ratio of the Sides
Ratio of the sides are in proportion to the one aligned with another point on another triangle
Ratio of the perimeters
All the ratios will reduce to 2/1
Ratio of the areas
All ratios will reduce to 4/1
How to find perimeter
Add the lengths of all the sides
Mid-Segment Theorem
The segment joining the midpoints of any two sides will be parallel to the third side and half its length
Proving triangles similar to AA
If two angles of one triangle are congruent to two angles of another, then the triangles must be similar
Proving triangles similar by SAS
States that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent
Proving triangles similar by SSS
If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar
Angle Bisector Theorem
Relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle
Altitude Rule
The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse
Leg Rule
Each leg of the hypotenuse of a right angled triangle is the mean proportional between the hypotenuse and part of the hypotenuse nearby that leg
Section Formula
Coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m:n
Radius
Any of the line segments from its center to its perimeter
Chord
Straight line segment whose endpoints both lie on the circle
Diameter
Any straight line segment that passes through the center of the circle and whose endpoints lie on the circle
Secant
A line that intersects two or more points on a curve
Tangent
A straight line that just touches the curve at that point
Arc
Closed segment of a curve
Minor Arc
The shorter arc joining two points on the circumference of a circle
Major Arc
The larger arc joining two points on the circumference of a circle
Semi-Circle
One-dimensional locus of points that forms half of a circle, arc always measures 180 degrees
Central Angle
Angle that forms when two radii meet at the center of a circle
Inscribed Angle
Angle formed by two chords in a circle which have a common endpoint
Angle Inscribed in a Semi-Circle
The angle measure will always be 90 degrees
Floating Angles
Angle inside a vertical angle and you add the angles on the outside
Tangent Radius
A tangent to a circle is perpendicular to the radius at the point of tangency
Common Tangent
Line that is tangent to each of two coplanar(in the same plane) circles
Tangent Chord Angle
An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc
Tangent Tangent Angle
Angle that is outside of the circle that is more wide of an angle than secant secant, half of the subtraction of the two angles near it
Secant Secant Angle
Angle is also outside of circle, but is less wide than the tangent tangent angle, half of subtraction of two angles near it
Tangent Secant Angle
Angle formed by a secant and a tangent intersecting in the interior of a circle is equal to one-half the difference of the measures of the intercepted arcs