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intersection
the points that two geometric figures share

intuition
drawing a conclusion through insight

inverse
relative to the statement “If P, then Q,” this statement has the form “If not P, then not Q”

isosceles trapezoid
a trapezoid that has two congruent legs(its nonparallel sides)

isosceles triangle
a triangle that has two congruent sides

kite
a quadrilateral that has two distinct pairs of congruent adjacent sides

lateral area
the sum of areas of the lateral faces of a solid orthe area of the curved lateral surface, excluding the base area(s) (as in prisms, pyramids, cylinders, and cones)

legs of isosceles triangle
the two congruent sides of the triangle

legs of right triangle
the two sides that form the right angle of the triangle

legs of trapezoid
the two nonparallel sides of the trapezoid

lemma
a theorem that is introduced and proved so that a later theorem can be proved

line of centers
the line (or line segment) that joins the centers of two circles

line segment
the part of a line determined by two points and all points on the line that lie between those two points

locus
the set of all points that satisfy a given condition or conditions

octahedron (regular)
a polyhedron with eight congruent faces that are equilateral triangles

opposite rays
two rays having a common end point and which together form a line

orthocenter of triangle
the point of concurrence for the three altitudes of the triangle

parallel lines (planes)
two lines in a plane (or two planes) that do not intersect

parallelogram
a quadrilateral that has two pairs of parallel sides

parallelepiped
a right rectangular prism; a box

pentagon
a polygon that has exactly five sides

perimeter of polygon
the sum of the lengths of the sides of the polygon

perpendicular bisector of line segment
a line (or part of aline) that is both perpendicular to a given line segment and bisects that line segment

perpendicular lines
two lines that intersect to form congruent adjacent angles

pi ( )
the constant ratio of the circumference C of a circle to the length of its diameter, this ratio is commonly approximated by the fraction or the decimal 3.1416

point of tangency (contact)
the point at which a tangent to a circle touches the circle

polygon
a plane figure whose sides are line segments that intersect only at their endpoints

polyhedron
a solid figure whose faces are polygons that intersect other faces along common sides of the polygons

postulate
a statement that is assumed to be true

Quadratic Formula
 the formula ,
 which provides solutions for the equation ,where a, b, and c are real numbers and

quadrilateral
a polygon that has exactly four sides

radian
the measure of a central angle of a circle whose intercepted arc has a length equal to the radius of the circle

radius
the line segment that joins the center of a circle (or sphere) to any point on the circle (or sphere)

ratio
a comparison between two quantities , generally written or a:b

ray
the part of a line that begins at a point and extends infinitely far in one direction

rectangle
a parallelogram that contains a right anglereflex angle an angle whose measure is between 180°and 360°

regular polygon
a polygon whose sides are congruent and whose interior angles are congruent

regular polyhedron
a polyhedron whose edges are congruent and whose faces are congruent

major arc
an arc whose measure is between 180° and 360°

means of a proportion
 the second and third terms of a proportion; in ,
 b and c are the means

median of trapezoid
the line segment that joins the midpoints of the two legs (nonparallel sides) of the trapezoid

median of triangle
the line segment joining a vertex of the triangle to the midpoint of the opposite side

midpoint
the point on a line segment (or arc) that separates the line segment (arc) into two congruent parts

minor arc
an arc whose measure is between 0° and 180°

nonagon
a polygon that has exactly nine sides

noncollinear points
three or more points that do not lie on the same line

noncoplanar points
four or more points that do not lie in the same plane

obtuse angle
an angle whose measure is between 90°and 180°

obtuse triangle
a triangle that has exactly one interior angle that is obtuse

octagon
a polygon that has exactly eight sides

regular prism
a right prism whose bases are regular polygons

regular pyramid
a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles

rhombus
a parallelogram with two congruent adjacent sides

right angle
an angle whose measure is exactly 90°

right circular cone
a cone in which the line segment joining the vertex of the cone to the center of the circular base is perpendicular to the base

right circular cylinder
a cylinder in which the line segment joining the centers of the circular bases is perpendicular to the plane of each base

right prism
a prism in which lateral edges are perpendicular to the base edges that they intersect

right triangle
a triangle in which exactly one interior angle is a right angle

scalene triangle
a triangle in which no two sides are congruent

secant
in a right triangle, the ratio

secant of circle
a line (or part of a line) that intersects a circle at two points

sector of circle
the plane region bounded by two radii of the circle and the arc that is intercepted by the central angle formed by those radii

segment of circle
the plane region bounded by a chord and a minor arc (major arc) that has the same endpoints as that chord semicircle the arc of

semicircle
the arc of a circle determined by a diameter; an arc of a circle whose measure is exactly 180°

set
any collection of objects, numbers, or points

similar polygons
polygons that have the same shape

sine
in a right triangle, the ratio

skew quadrilateral
a quadrilateral whose sides do not all lie in one plane

slant height of cone
any line segment joining the vertex of the cone to a point on the circular base

slant height of regular pyramid
a line segment joining the vertex of the pyramid to the midpoint of a base edge of the pyramid

slope
a measure of the steepness of a line; in the rectangular coordinate system, the slope m of the line through (x _{1},y _{1}) and (x _{2},y _{2}) is , where x _{1} x _{2}

sphere
the set of points in space that are at a fixed distance from a given point (the center of the sphere)

straight angle
an angle whose measure is exactly 180°; an angle whose sides are opposite rays

straightedge
an idealized instrument used to construct parts of lines

volume
the measurement, in cubic units, of the amount of space within a bounded region of space

vertical angles
a pair of angles that lie in opposite positions when formed by two intersecting lines

vertex of polyhedron
any point at which three edges of the polyhedron meet

vertex of polygon
any point at which two sides of the polygon meet

vertex of isosceles triangle
the point at which the two congruent sides of the triangle meet

vertex of angle
the point at which the two sides of the angle meet

vertex angle of isosceles triangle
the angle formed by the two congruent sides of the triangle

valid argument
an argument in which the conclusion follows logically from previously stated (and accepted) premises or assumptions

union
the joining together of any two sets, such as geometric figures

triangle inequality
a statement that the sum of the lengths of two sides of a triangle cannot be greater than the length of the third side

triangle
a polygon that has exactly three sides

trapezoid
a quadrilateral having exactly two parallel sides

transversal
a line that intersects two or more lines, intersecting each at one point

torus
a threedimensional solid that has a “doughnut” shape

theorem
a statement that follows logically from previous definitions and principles; a statement that can be proved

tetrahedron (regular)
a fourfaced solid in which the faces are congruent equilateral triangles

tangent line of circle
a line (or part of a line) that touches acircle at only one point

tangent circles
two circles that have one point in common;the circles may be externally tangent or internally tangent

tangent
in a right triangle, the ratio

symmetry with respect to a point (P )
figure for which everypoint A has a second point C on the figure for which P is the midpoint of

symmetry with respect to a line (l)
figure for which everypoint A has a second point B on the figure for which l is the perpendicular bisector of

surface area
the measure of the total area of a solid; the sum of the lateral area and base area in many solid figures.

supplementary angles
two angles whose sum of measuresis 180°

