y minus y one equals slope (m) times x minus x one.

Back

Triangles classified by angles

Front

acute triangles have 3 acute angles.
right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.

Back

Midpoint formula

Front

x one plus x two divided by two is the x coordinate.
y one plus y two divided by two is the y coordinate.

Back

Slope

Front

from left to right. up the hill is positive slope. down the hill is negative slope. a horizontal line has 0 slope and a verical line as an undefined slope.

Back

Finding the slope and y intercept of a line

Front

y must be positive and isolated on one side of the equation.

Back

Mid segment of a triangle

Front

a mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the side not containing the 2 midpoints.

Back

Lengths of 2 intersecting secants

Front

the whole length of the first secant times the outside length of the first secant equals the whole length of the second secant times the outside length of the second secant.

Back

Complementary angles

Front

2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.

Back

Median

Front

bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.

Back

Angle formed by 2 secants

Front

is equal to the major arc minus the minor arc divided by 2.

Back

Distance formula

Front

the square root of x two minus x one squared plus y two minus y one squared.

Back

Isosceles triangles

Front

sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.

Back

Angle formed by 2 chords intersecting in a circle

Front

is equal to the sum of the arcs divided by 2.

Back

Area of a circle

Front

pi times radius squared.

Back

Secant

Front

intersects a circle in 2 places.

Back

Lengths of an intersecting diameter and chord that meet at right angles (perpendicular)

Front

if a diameter meets a chord at a right angle (perpendicular), the diameter divides the chord into 2 equal parts.

Back

Adjacent angles

Front

share a common vertex, a common side, but not common interior points.

Back

C.P.C.T.C.

Front

corresponding parts of congruent triangles are congruent.

Back

Angle bisector

Front

bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.

Back

Perpendicular bisector

Front

bisects and makes a right angle with a side of a triangle.They meet in a triangle at a point called the circumcenter.

Back

Lengths of 2 intersecting chords

Front

part of the first chord times the other part of the first chord equals a part of the second chord times the other part of the second chord.

Back

Tangent

Front

intersects a circle in only 1 place.

Back

Slope intercept form of a line

Front

y equals slope (m) times x plus the y intercept (b)

Back

Triangle inequality theorem

Front

the sum of 2 sides of a triangle must be greater than the 3rd side.

Back

Alternate interior angles

Front

alternate interior angles are congruent.

Back

Intersection of a tangent and a radius

Front

form right angles when they intersect.

Back

Corresponding angles

Front

corresponding angles are congruent.

Back

Equation of a circle

Front

x minus h squared plus y minus k squared equals radius squared.

Back

Slope formula

Front

y two minus y one divided by x two minus x one.
rise over run.

Back

Right triangle ratios

Front

Back

Altitude

Front

makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.

Back

Lengths of intersecting tangents

Front

Tangents to a circle sharing a common vertex are equal.

Back

Angle formed by a secant and a tangent

Front

is equal to the major arc minus the minor arc divided by 2.

Back

Similar triangles

Front

angles in similar (∼) triangles are congruent.
sides are in proportion.
angles are in a proportion of one to one. (1:1)

Back

Angles

Front

acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles are between 90 and 180 degrees. Straight angles are 180 degrees and reflex angles are greater than 180 degrees.

Back

Supplementary angles

Front

2 angles when added together that equal 180 degrees.They do not have to be adjacent angles.

Back

Lengths of an instersecting secant and tangent

Front

the whole length of the first secant times the outside length of the first secant equals the length of the tangent squared.

Back

Angle formed by two tangents

Front

is equal to the major arc minus the minor arc divided by 2.

Back

Pythagorean theorem

Front

a squared plus b squared equals c squared.
the hypotenuse is always c.

Back

Triangles classified by sides

Front

scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.

Back

Central angle

Front

is equal to its intercepted arc.

Back

Vertical angles

Front

vertical angles are congruent.

Back

Exterior angle of a triangle

Front

the exterior angle of a triangle equals the sum of the 2 opposite interior angles.

Back

Sum of the angles in a triangle

Front

the 3 angles of a triangle add up to 180 degrees.

Back

Inscribed angle

Front

is equal to ½ its intercepted arc.

Back

Proving triangles congruent

Front

can not be angle angle side (A.S.S.) or side side angle(S.S.A.).

Back

Circumference of a circle

Front

2 times pi times radius or pi times diameter.

Back

Proving triangles similar

Front

need only 2 angles to be congruent to probe 2 triangles similar.

Back

Find the endpoint of a line given the midpoint and the other endpoint

Front

the integers added to the coordinates of C to get the coordinates of M are added to the coordinates of M to get the coordinates of D.

Back

Proving right triangles congruent

Front

hypotenuse leg.

Back

Section 2

(50 cards)

Parallelograms

Front

opposite sides are parallel.
opposite sides and angles are congruent.
consecutive angles are supplemental (add to 180).
diagonals bisect each other.

Back

Area of a trapezoid

Front

½ times the height times the sum of the 2 parallel sides.

Back

Line

Front

has no thickness, but it extends forever in both directions.

Back

Rectangle

Front

opposite sides are parallel.
opposite sides are congruent.
contains 4 right angles.
diagonals are congruent and bisect each other.

Back

Reflection over the x axis

Front

change the sign of the y coordinate.

Back

Lateral surface area of a cylinder

Front

2 times pi times the radius times the height.

Back

Volume of a rectangular prism

Front

length times width times height.

Back

Reflection over the line y=x

Front

switch the x and y coordinates.

Back

Rhombus

Front

Opposite sides are parallel.
All sides are congruent.
Diagonals are congruent and Perpendicular(make right angles).
Diagonals bisect each other and the Angles of the rhombus.

Back

Perimeter

Front

distance around the outside of a polygon.

Back

Opposite isometry

Front

distance is preserved(same). direction is reversed(opposite).

Back

Area of a rectangle

Front

Base times height or
length times width.

Back

Rotation of 270 degrees

Front

graph the coordinate. rotate the graph 270 degrees counter clockwise and read the point.

Back

Axis of symmetry

Front

the equation for axis of symmetry is x equals negative b divided by two times a.

Back

Volume of a cone

Front

one third times pi times the radius squared times the height.

Back

Translation

Front

add the 2 integers to the orginal coordinate. add the first integer to the x coordinate and the second integer to the y coordinate.

Back

Rotation of 180 degrees

Front

graph the coordinate. rotate the graph 180 degrees counter clockwise and read the point.

Back

Disjunctions

Front

or (∨) is only false when both statements are false.

Back

Plane

Front

has no thickness and extends forever in all directions.

Back

Area of a triangle

Front

Base times the height divided by 2.

Back

Transformations

Front

Dilations are a capital D.
Reflections are a lower case r.
Rotations are a capital R.
Translations are a capital T.

Back

Isosceles trapezoid

Front

One set of parallel sides.
Non-parallel sides are congruent.
Base angles are congruent.
Diagonals are congruent.

Back

Median of a trapezoid

Front

The top parallel side plus the other parallel side divided by 2.

Back

Area of a parallelogram

Front

Base times the height

Back

Square

Front

opposite sides are parallel.
all sides are congruent and meet at right angles.
diagonals are congruent and perpendicular(make right angles).
diagonals bisect each other and the angles of the square.

Back

Slopes of perpendicular lines

Front

the slopes are negative reciprocals.
to find the negative reciprocal make the slope a fraction, flip it, and change the sign.

Back

Reflection over the y axis

Front

change the sign of the x coordinate.

Back

Rotation of 90 degrees

Front

graph the coordinate. rotate the graph 90 degrees counter clockwise and read the new point.

Back

Logic statements

Front

for the converse switch the two statements.
for the inverse negate the two statements.
for the contrapositive and logically equivalent, switch and negate the two statements.

Back

Area of a square

Front

Base times height or side squared.

Back

Volume of a pyramid

Front

one third times the area of the base times the height.
the base could be a triangle, rectangle, or square

Back

Biconditional

Front

if and only if (↔) is true when the two statements have the same truth value.

Back

Surface area of a sphere

Front

4 times pi times the radius squared.

Back

Lateral surface area of a cone

Front

pi times the radius times the slant height.

Back

Polygons

Front

a triangle has 3 sides. a quadrilateral has 4 sides. a pentagon has 5 sides. a hexagon has 6 sides. a octagon has 8 sides. a decagon has 10 sides.

Back

Parallel and perpendicular lines

Front

Back

Slopes of parallel lines

Front

have the same slope and a different y intercept.

Back

Conjuntions

Front

and (∧) is true only when both are statements are true.

Back

Glide reflection

Front

a refection combined with a translation.

Back

Dilation

Front

Multiply both coordinates by the scale factor.

Back

Direct isometry

Front

distance is preserved(same). direction is preserved(same)

Back

Conditionals

Front

if then (→) is only false when the first statment is true and the second statement is false.

Back

Volume of a sphere

Front

four thirds times pi times the radius to the thrid power.

Back

Surface area of a rectangular prism

Front

2 times the sum of the length times the width, the length times the height. and the width times the height.

Back

Isometry

Front

the lengths of corresponding line segments remain the same.

Back

Trapezoid

Front

One set of parallel sides.

Back

Area of a rhombus

Front

Base times the height

Back

Surface area of a cylinder

Front

2 times pi times radius times the sum of the height and radius.

Back

Volume of a cylinder

Front

pi times radius squared times the height.

Back

Formula for angles of polygons

Front

the sum of the interior angles equals the number of sides minus 2 times 180 degrees.
the sum of the exterior angles equal 360 degrees.

Back

Section 3

(10 cards)

Point

Front

has no length, width, or thickness. It is indentified by a capital letter.

Back

Skew Lines

Front

are lines on different planes that never touch.

Back

Locus of 2 points

Front

is the perpendicular bisector between the 2 points.

Back

Collinear points

Front

are points that lie on the same line

Back

Locus of a single point

Front

is a circle around the point that is an equal distance from the point.

Back

Locus of a single line

Front

is a parallel line above the line and a parallel line below the line that are both an equal distance from the original line.

Back

Locus of 2 intersecting lines

Front

is the angle bisectors of the 4 angles formed by the intersecting lines.

Back

Locus of 2 lines

Front

is a straight line directly between and an equal distant from the 2 lines.