Download Geometry Dictionary

Sasha Vasserman
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Two triangles are similar if two pairs of
corresponding angles are congruent
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Two triangles are congruent if two pairs of
corresponding angles are congruent and a
non-included pair of corresponding sides are
congruent
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The x-coordinate of a point in the coordinate
plane
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For a number x, denoted by |x |, its distance
from 0 on the number line. Thus, |x| always
represents a nonnegative number
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An angle whose degree measure is < 0 and >
90
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A triangle with three acute angles
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Two angles that have the same vertex and
share one side, but do not have any inferior
points in common
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Pairs of angles formed when a transversal
intersects two lines. The two angles ion each
pair are between the two lines, have different
vertices, and lie on opposite sides of the
transversal
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A segment that is perpendicular to the side of
the figure to which it is drawn
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The union of two rays that have the same end
point
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A line or any part of a line that contains the
vertex of an angle and that divides the angle
into two congruent angles. An angle has
exactly one angle bisector
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An angle formed by a horizontal ray of sight
and the ray that is the line of sight to an
object below the horizontal ray
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An angle formed by a horizontal ray of sight
and the ray that is the line of sight to an
object above the horizontal ray
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For a regular polygon, the radius of its
inscribed circle
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The minor arc of a circle whose end points
are the end points of a chord. If the chord is a
diameter, then either semicircle is an arc of
the diameter
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For a plane geometric figure, the number of
square units it contains
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Two triangles are congruent if two pairs of
corresponding angles are congruent and the
sides included by these angles are congruent
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The congruent angles that lie opposite the
congruent sides of an isosceles triangle
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The non-congruent side of the isosceles
triangle
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The parallel sides of a trapezoid
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A term that refers to the order of three
collinear points. If A, B, and C are three
different collinear points, point C us between
points A and b if AC + CB = AB
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To divide into two equal parts
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The common center of the circles inscribed
and circumscribed in the polygon
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An angle whose vertex is at the center of a
circle, and whose sides are radii
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An angle whose vertex is the center if the
regular polygon and whose sides terminate at
consecutive vertices of the polygon
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The point at which three medians of the
triangle intersect
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A segment whose end points are on the circle
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The set of all points in a plane at a fixed
distance from a given point called the center.
The fixed distance is called the radius of the
circle. An equation of a circle with center at
point (h, k) and radius length r is (x - h²) +
(y- k)² = r²
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The distance around a circle
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A circle that passes through each vertex of
the polygon
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A polygon that has all of its sides tangent to
the circle
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Points that lie on the same line
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A line that is tangent to both circles, and
does not intersect the line segment whose
end points are the centers of the two circles
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A line that is tangent to both circles, and
intersects the line segment whose end points
are the centers of the two circles
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Two angles whose measures add up to 90°
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A sequence of two or more transformations in
which each transformation after the first is
preformed on the image of the
transformation that was applied before it
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Circles in the same plane that have the same
center but have radii of different lengths
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Angles that have the same measure
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Circles with congruent radii
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Line segments that have the same length
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Polygons with the same number of sides that
have the same size and same shape. The
symbol for congruence is ≅
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Triangles whose vertices can be paired so that any
one on the following conditions is true: (1) the sides
of one triangle are congruent to the corresponding
sides of the other triangle (SSS ≅ SSS); (2) two sides
and the included angle of one triangle are congruent
to the corresponding parts of the other triangle (SAS
≅ SAS); (3) two angles and the included side of one
triangle are congruent to the corresponding parts of
the other triangle (ASA ≅ ASA); (4) two angles and the
side opposite one of these angles of one triangle are
congruent to the corresponding parts of the other
triangle ( AAS ≅ AAS). Two right triangles are
congruent if the hypotenuse and a leg of one right
triangle are congruent to the corresponding parts the
other triangle (Hy – Leg ≅ Hy – leg)
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Another conditional statement formed by
interchanging the hypothesis (“Given”) with
the conclusion (“To Prove”) of the original
statement
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A polygon each of whose interior angles
measures less than 180°
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A plane that is divided into four equal regions,
called quadrants, by a horizontal number line
and a vertical number line, called axes,
intersecting at their zero points, called the origin.
Each point in a coordinate plane is located by an
ordered pair of numbers of the form (x, y). The
first member, x, of the ordered pair gives the
directed distance of the zero point of the x-axis
(horizontal). The second member, y, of the
ordered pair gives the directed distance of the
point from the zero point of the y-axis
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A theorem that can easily be proved by
means of a closely related theorem
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Pairs of angles formed when a transversal
intersects two lines. The two angles in each
pair lie on the same side of the transversal,
but one angle is between the two lines, and
the other is exterior to the two lines
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The ratio of the length of the leg that is
adjacent to the acute angle to the length of
the hypothenuse
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A polygon with 10 sides
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A step-by-step process by which a set of
accepted facts is used to arrive at a
conclusion
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A unit of angle measure. One degree is the
measure of an angle formed by 1/360 of one
complete rotation of a ray about its end point
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A line segment whose end points are
nonconsecutive vertices of the polygon
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A chord of the circle that contains the center
of the circle
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A size transformation that produces an image
similar to the original figure
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An isometry that pressserves orientation
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A formula used to find the length of the
segment determined by two points in the
coordinate plane. The distance d between two
points , A and B, is given by the formula d =
the square root of ((X of point B – X of point
A)squared + (Y of point B – Y of point A)
squared)
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The length of the perpendicular segment
from the point to the line
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A polygon with 12 sides
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A polygon in which all the angles have the
same measure
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A triangle in which all three angles have the
same measure
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Having the same distance
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A polygon in which all the sides have the
same length
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A triangle whose three sides have the same
length
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An angle formed by a side of the polygon and
the extension of an adjacent side of the
polygon
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Tangent circles that lie on opposite sides of
the common tangent
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The first and fourth terms in a proportion. In
the proportion a over b = c over d, a and d
are the extremes
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The composition of a reflection in a line and a
translation in the direction parallel to the
reflecting line
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The set of points in a plane that lie on one
side of a line
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A polygon with six sides
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The side of a right triangle that is opposite to
the right angle
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The point at which three bisectors of the
triangle intersect
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A method of proof in which each possibility
except the one that needs to be proved is
eliminated by showing that it contradicts
some known or given fact
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An angle whose vertex lies on the circle and
whose sides are chords of the circle
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A circle that is tangent to each side of the
polygon
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A polygon that has all of its vertices on a
circle
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Tangent circles that lie on one side of the
common tangent
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A transformation that produces an image
congruent to the original figure
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A trapezoid whose nonparallel sides called
legs, have the same length
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A triangle with two sides, called legs that
have the same length
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Either of the two sides of the right triangle
that are not opposite the right angle
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A term undefined in geometry; a line can be
described as a continuous set of points
forming a straight path that extends
indefinitely in two opposite directions
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The line segment whose end points are the
centers of the circles
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Part of a line that consists of two different
points on a line called end points, and the set
of all points on the line that ate between
them. AB refers to the distance of a line
segment with end points A and B, whereas AB
with a line of it refers to the segment itself
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When a line can be drawn that divides the
figure into two parts that coincide when
folded along the line
The set of all points, and only those points,
that satisfy a given condition
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An arc of a circle whose degree measure is
greater than 180°
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The two middle terms of a proportion. In the
proportion a over b = c over d, then either b
or c are called the mean proportional between
a and d
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A line segment whose end points are the
midpoints of the legs of the trapezoid
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A line segment whose end points are a vertex
of the triangle and the midpoint of the side
opposite that vertex
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A formula used to find the coordinates of the
midpoint of a line segment in the coordinate
plane. The midpoint of a line segment whose
points are A(x, y) and B(X, Y) is ( (x + X over
2) + ( y + Y) over 2))
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The point on a line segment that divides the
segment into two segments that have the
same length
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An arc of a circle whose degree measure is
less than 180°
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An angle whose degree measure is greater
than 90° and less than 180°
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A triangle that contains an obtuse angle
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A polygon with eight sides
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An isometry that reverses orientation
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Two rays that have the same end point and
form a line
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The y-coordinate of a point in the coordinate
plane
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The zero point on a number line
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The point at which the three altitudes of the
triangle intersect
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Lines in the same plane that do not intersect
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A quadrilateral that has two pairs of parallel
sides
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A polygon with five sides
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The sum of the lengths of the sides of the
polygon
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A line, ray, or line segment that is
perpendicular to the segment at its midpoint
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Two lines that intersect at 90° angles
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A term undefined in geometry; a plane can be
described as a flat surface that extends
indefinitely in all directions
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A term undefined in geometry; a point can be
described as a dot with no size that indicates
location
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A figure with 180° rotational symmetry
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A closed figure in a plane whose sides are
line segments that intersect at their end
points
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A statement whose truth is accepted without
proof
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An equation that states that two ratios are
equal. In a proportion, the product of the
means equals the product of the extremes
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In a right triangle, the sum of the squares of
the lengths of the legs is equal to the square
of the length of the hypotenuse
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One of the four equal rectangular regions into
which the coordinate plane is divided
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A polygon with four sides
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A line segment whose end points are the
center of the circle and any point on a circle
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The radius of its circumscribed circle
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A comparison of two numbers by division.
The ratio of a to b can be represented by the
fraction a over b, provided that b is not equal
to zero
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The constant ratio of the lengths of any two
corresponding sides
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The part of a line that consists of a fixed
point, called an end point, and the set of all
points on one side of the end point
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The number that, when multiplied by the
original number, gives 1. For example, the
reciprocal over 1 over 5 is 5 over 1, AKA, 5. 5
over 1 times 1 over 5 equals 1
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A parallelogram with four right angles
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An isometry that “flips” a figure over a line
while reversing orientation
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A parallelogram with four sides that have the
same length
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An angle whose degree measure is 90°
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A triangle that contains a right angle
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An isometry that “turns” a figure a specified
number of degrees in a given direction
(clockwise or counterclockwise) about some
fixed point called the center of rotation
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A figure has rotational symmetry if it
coincides with its image for some rotation of
180° or less
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Two triangles are congruent if two pairs of
corresponding sides are congruent and the
angles formed by these sides are congruent
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A triangle in which no two sides have the
same length
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A line that intersects the circle in two
different points
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An arc whose end points are a diameter of
the circle
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Figures that have the same shape but may
have different sizes. Two polygons with the
same number of sides are similar if
corresponding angles are congruent and the
lengths of corresponding sides are in
proportion
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The ratio of the length of the leg that is
opposite the acute angle to the length of the
hypotenuse
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A numerical measure of the steepness of a
non-vertical line. The slope of a line is the
difference of the coordinates of any two
different points on the line divided by the
difference of the corresponding
x-coordinates of the two points. The slope of
a horizontal line is 0, and the slope of a
vertical line is undefined
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A formula used to calculate the slope of a
non-vertical line when the coordinates of two
points on the line are given. The slope, m, of
a non-vertical line that contains points x and
y and X and Y is given by the formula m = Y –
y over X - x
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An equation that has the form y = m * x + b,
where m is the slope of the line, b is the
y-coordinate of the point at which the line
crosses the y-axis
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A rectangle all of whose sides have the same
length
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Two triangles are congruent if three pairs of
corresponding sides are congruent
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Two angles whose measures add up to 180°
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Circles in the same plane that are tangent to
the same line at the same point
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The ratio of the length of the leg that is
opposite a given acute angle to the length of
the leg that is adjacent to the same angle
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A line that intersects the circle in exactly one
point, called the point of tangency
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A generalization that can be proved
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A mapping of the elements of two sets where
the elements are points such that each point
of the object is mapped onto exactly one
point called its image and each image point
corresponds to exactly one point of the
original object called the preimage
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An isometry that “slides” all points of a figure
the same distance in the same direction
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A line that intersects two lines at different
points
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A quadrilateral with exactly one pair of
parallel lines
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A polygon with three sides
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A term that can be described but is so basic
that it cannot be defined. The terms point,
line, and plane are undefined in geometry
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The point at which two sides of the polygon
intersect
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The angle formed by the congruent sides of
the isosceles triangle
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Pairs of non-adjacent ( opposite ) angles
formed by two intersecting lines
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The capacity of a solid figure as measured by
the number of cubic units it contains
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The horizontal number line in the coordinate
plane
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The first number in the ordered pair that
represents the coordinates of a point in the
coordinate plane. The x-coordinate gives the
directed horizontal distance of the point from
the origin
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The vertical number line in the coordinate
plane
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The second number in the ordered pair that
represents the coordinates of a point in the
coordinate plane. The y-coordinate gives the
directed vertical distance of the point from
the origin
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The y-coordinate of the point at which a
non-vertical line crosses the y-axis