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Gravity
Terms in this set (129)
congruent
figures with the same shape, angles, sizes, sides; two or more figures with corresponding sides and angles that are equal in measure; refers to shape and size of geometric figure
similar
two or more figures with corresponding angles that are equal in measure and corresponding sides that are proportional
pre-image
original figure that is to be transformed
image
figure that is formed when each point in an original figure is moved in a specific way (mapped)
vector
directed line segment that indicates magnitude and direction; show distance and direction of a mapping from pre-image to image
composite transformation
more than one transformation is performed on a figure
prime (')
image point with its pre-image point (')
rigid motion
movement where distance and angle measure are both preserved; pre-image and image are congruent; ISOMETRY (i.e. translations, reflections, rotations)
non-rigid motion
dilation; movement where distance is not preserved but angle measure is preserved; pre-image and image are similar; corresponding angles are congruent and corresponding sides are proportional
invariant
points or properties that do not change when the pre-image is mapped onto its image
notation, rule
type of transformation required indicated by using a letter to show the type of transformation (sometimes in front, over or under)
line reflection
rigid motion; opposite isometry; each sides of ... is a "mirror image" of the other side; distance, angle measure, collinearity are invariant
translation
shift of the figure in the x or horizontal direction and/or shift in the y or vertical direction; each point is translated the same distance and direction; rigid motion (pre-image and image are congruent, preserves parallelism); DIRECT ISOMETRY
rotation
turning or a figure around a point for a specified number of degrees; each point in image is same distance from center of rotation (always counterclockwise unless stated -- negative degree marking indicated clockwise)
glide reflection
composite transformation in which a figure is reflected through a line and translated along that line in a direction parallel to the line of reflection
diagram
figure that represents information given in the problem
axiom, postulate
proposition that is a starting point from which further logical steps can be determined; used to prove theorems (i.e. "If two parallel lines are cut by a transversal, corresponding angles are congruent")
theorem
proposition that can be proved logically using principles of deduction (i.e. "The sum of the angles of a triangle is 180 degrees)
reason
justification for using a statement (postulates, axioms, theorems, corollaries, properties, definitions, formulas)
corresponding parts
angles/sides of a polygon that are in matching positions with another polygon (used with similar or congruent polygons)
properties of equality
used as reasons in deductive reasoning geometry proofs
addition property of equality
if a=b and c=d, then a+c=b+d; if equal quantities are added to equal quantities, the sums are equal
subtraction property of equality
if a=b and c=d, then a-c=b-d; if equal quantities are subtracted from equal quantities, the differences are equal
multiplication property of equality
if a=b, then ac=bc; if equal quantities are multiplied by equal quantities, the products are equal
reflexive property of equality
anything that is equal to itself (numbers, line segments, angles)
symmetric property of equality
if a=b, then b=a
transitive property of equality
if a=b and b-c, then a=c
substitution property of equality
if a=b, then a can be replaced by b and b can be replaced by a (if a+b=c and m+n=c, then a+b=m+n)
partition postulate
the whole is equal to the sum of its parts
betweenness
if point B is between points A and C, then AB+BC=AC
distance
length of segment between two points
perpendicular distance
length of the perpendicular segment from point to a line; "default" (always use this unless directed)
equidistant
"equally distant"
midpoint
if point M, on line segment AC, divides the segment into two congruent segments, AM is congruent to MC, then point M is the ... of AC
angle bisector
divides an angle into two congruent angles
segment bisector
divides a line segment into two congruent line segments
dilation
type of transformation that is a non-rigid motion; similarity; does NOT preserve distance; angle measure is preserved; can be used when showing two figures are similar to each other
triangle
polygon with three sides
180
sum of angles in a triangle (degrees)
acute
type of triangle - each of the three angles is less than 90 degrees
right
type of triangle - one angle is 90 degrees, the other two are a complementary pair
obtuse
type of triangle - one angle is greater than 90 degrees and less than 180 degrees
equiangular
type of triangle - all three angles are congruent (60 degrees each)
scalene
type of triangle - none of the three sides are congruent
isosceles
type of triangle - two sides are congruent
equilateral
type of triangle - all three sides are congruent
hypotenuse-leg (theorem)
If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of the other, the two triangles are congruent (triangles must be identified as right triangles before)
pythagorean theorem
theorem - if a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs; c is the hypotenuse and a/b are the legs; side c is the longest side (a2+b2=c2); used to find missing side of triangle and prove whether triangle is right or not
ASA, angle side angle
If two angles and the included side in one triangle are congruent to the corresponding parts of the other, the triangles are congruent
SAS, side angle side
If two sides and the included angle in one triangle are congruent to the corresponding parts of the other, the triangles are congruent
SSS, side side side
if three sides of one triangle are congruent to three sides of another, the two triangles are congruent
AAS, angle angle side
if two angles and a non-included side of one triangle are congruent to the corresponding parts of another, the triangles are congruent
polygon
a plane figure in which all sides are line segments; named by number of sides; generally, ... with "n" sides is called a "n-gon"
regular polygon
figure in which all sides are congruent and all angles are congruent
interior angles
formula S = (n-2)(180) gives the sum of the .... of any convex polygon
360
sum of the exterior angles of any convex polygon
congruent polygons
two (or more) polygons that have corresponding sides that are congruent and corresponding angles that are congruent
quadrilateral
four straight sides and four interior angles, sum of the interior angles is 360 degrees
trapezoid
quadrilateral with...
at least one pair of parallel sides
parallelogram
quadrilateral with...
2 pairs of parallel sides
opposite sides and angles are congruent
diagonals bisect each other
diagonals cut into 2 congruent triangles
consecutive angles are supplementary
rectangle
quadrilateral with...
congruent diagonals
4 right angles
rhombus
quadrilateral with...
4 congruent sides
perpendicular diagonals
square
quadrilateral with...
four congruent sides
four 90 degree angles
perpendicular and congruent diagonals
trigonometric value
ratio of lengths of two sides of a triangle based on measure of angle involved
right triangle
triangle containing one right angle
acute angles
other two angles in a right triangle; less than 90 degrees
hypotenuse
side directly across from the right angle of a right triangle; longest side of the triangle
legs
two sides of triangle that meet to form right angle
Sin
ratio of the side opposite to the given angle to the hypotenuse of the right triangle (trig function)
Cos
ratio of the side adjacent to the given angle to the hypotenuse of the right triangle (trig function)
Tan
ratio of the side opposite to the given angle to the adjacent side (trig function)
cylinder
a solid geometric figure with straight parallel sides and a circular or oval cross section
Cavalieri's Principle
If two figures have equal altitudes and equal areas for each parallel plane that can be cut through them, their volumes are equal
1/3Bh
volume of a cone
1/3Bh
volume of a pyramid
solid
closed figure, usually including its interior space
polyhedron
closed figure with faces that are planar (flat); faces meet edges which meet at vertices
edge
point where faces meet on line segments
vertice
point where edges meet
cross section
2-dimensional figure that is created when plane is passed through polyhedron; can be many shapes
prism
polyhedron with parallel congruent bases which are both polygons and lateral faces that are all parallelograms; lateral edges are congruent and parallel
cube
prism whose faces are all congruent squares (i.e. a die)
rectangular prism
prism whose faces are rectnaglse
triangular prism
prism with 2 parallel bases are triangles while other sides are rectangles
pyramid
polyhedron with polygon for base; lateral sides are triangles and meet are vertex/apex
cone
circular base and a curved surface for sides which meet in a single vertex opposite the base
sphere
three dimensional curved figure made up of all points equidistant from center
origin
intersection of the two axes at (0,0)
y-intercept
y-value at the point where the graphed line crosses the y-axis; often used as a starting point when graphing equations from slope-intercept form of equation
x-intercept
x-value of the point where a graphed line crosses the x-axis
slope
"steepness and direction" of the slant of a line on a graph; ratio of the vertical change in line to the horizontal change in the line; rise over run; written as fraction; "m"
slope formula
m= y2 - y1 / x2 - x1
slope intercept form
y=mx+b
vertical line
line created when slope is undefined
horizontal line
line created when slope equals zero
collinear points
two or more points that are on the same line
parallel
if two lines have the same slope, the lines are...
perpendicular
if two lines have negative reciprocals of each other, the lines are...
distance formula
used to find length of line segment that is not parallel to either axis; used to find areas and perimeters of polygons on coordinate plane; formula: SQUARE ROOT of (x2-x1)^2 + (y2-y1)^2
midpoint formula
to show line segments are congruent or line segment is bisected by another line; formula: (x2+x1 divided by 2, y2+y1 divided by 2)
focus
point inside the curve of a parabola
parabola
symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side (y = ax^2 + bx + c)
circle
round plane figure whose circumference consists of points equidistant from a fixed point (the center); measured in degrees; 360 degrees
radius
line segment from any point on the circle to the center
diameter
line segment from any point on the circle that goes through the center to another point on the circle
circumference
distance around the edge of the circle; 2(pie)r; (pie)d
area
number of unit squares that can be contained within it
subtend
when end points of an arc are formed by the intersection of the rays of an angle and the circle, the rays ... the arc; "cut off"
sector
portion of a circle bordered by two radii and an arc between them
arc
part of circumference; can be measured in degrees
minor arc
arc that measures < 180 degrees
major arc
arc that measures > 180 degrees
semi-circle
arc that measures 180; its points on the circle are the endpoints of a diameter of the circle
chord
segment that connects two points on a circle; interior of circle
tangent
line that extends from a point outside the circle to the circle, touching the circle at exactly one point; does not center circle
secant
line that passes through two points on a circle; connects a point outside the circle, intersects the circle and goes across it to another point on the other side of the circle
central angle
only angle in the group of angles related to circles that is equal to the arc it cuts off
inscribed angle
angle formed by two chords in a circle which have a common endpoint; 1/2 the measure of the arc it intercepts
incenter
point of concurrency of the three angle bisectors of a triangle; inside triangle; equidistant from each side of the triangle
circumcenter
intersection of the perpendicular bisectors of the sides of a triangle; intersection can be inside or outside triangle; vertices of triangle are equidistant from this point
alternate interior angles are congruent
two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Interior angles on the same side of the transversal are supplementary.
two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.
alternate exterior angles congruent
two parallel lines are cut by a transversal, then alternate exterior angles ate congruent.
corresponding angles
two parallel lines are cut by a transversal, then corresponding angles are congruent.
vertical angles
A pair of opposite congruent angles formed by intersecting lines
The lines are parallel #1
two lines are cut by a transversal such that a pair of corresponding angles are congruent,then the lines are parallel
The lines are parallel #2
two lines are cut by a transversal such that a pair of interior angles on the same side of the transversal or supplementary then the lines are parallel
The lines are parallel #3
if two lines are cut by a transversal such that a pair of alternate exterior angles are congruent then the lines are parallel
parallel postulate
through a point not on a line, there is exactly one line parallel to the given line
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