CollegeGeometry1.2

the points that two geometric figures share

drawing a conclusion through insight

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

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

a triangle that has two congruent sides

a quadrilateral that has two distinct pairs of congruent adjacent sides

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)

the two congruent sides of the triangle

the two sides that form the right angle of the triangle

the two nonparallel sides of the trapezoid

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

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

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

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

a polyhedron with eight congruent faces that are equilateral triangles

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

the point of concurrence for the three altitudes of the triangle

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

a quadrilateral that has two pairs of parallel sides

a right rectangular prism; a box

a polygon that has exactly five sides

the sum of the lengths of the sides of the polygon

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

two lines that intersect to form congruent adjacent angles

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

the point at which a tangent to a circle touches the circle

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

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

a statement that is assumed to be true

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

a polygon that has exactly four sides

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

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

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

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

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

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

a polyhedron whose edges are congruent and whose faces are congruent

an arc whose measure is between 180° and 360°

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

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

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

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

an arc whose measure is between 0° and 180°

a polygon that has exactly nine sides

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

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

an angle whose measure is between 90°and 180°

a triangle that has exactly one interior angle that is obtuse

a polygon that has exactly eight sides

a right prism whose bases are regular polygons

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

a parallelogram with two congruent adjacent sides

an angle whose measure is exactly 90°

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

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

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

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

a triangle in which no two sides are congruent

in a right triangle, the ratio

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

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

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

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

any collection of objects, numbers, or points

polygons that have the same shape

in a right triangle, the ratio

a quadrilateral whose sides do not all lie in one plane

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

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

a measure of the steepness of a line; in the rectangular coordinate system, the slope m of the line through (x₁,y₁) and (x₂,y₂) is , where x₁ x₂

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

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

an idealized instrument used to construct parts of lines

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

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

any point at which three edges of the polyhedron meet

any point at which two sides of the polygon meet

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

the point at which the two sides of the angle meet

the angle formed by the two congruent sides of the triangle

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

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

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

a polygon that has exactly three sides

a quadrilateral having exactly two parallel sides

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

a three-dimensional solid that has a “doughnut” shape

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

a four-faced solid in which the faces are congruent equilateral triangles

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

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

in a right triangle, the ratio

figure for which everypoint A has a second point C on the figure for which P is the midpoint of

figure for which everypoint A has a second point B on the figure for which l is the perpendicular bisector of

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

two angles whose sum of measuresis 180°