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.