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Inductive Reasoning

A type of reasoning that reaches conclusions based on a pattern of specific examples or past events.

Conjecture

A conclusion reached by using inductive reasoning.

Counterexample

A particular example or instance of the statement that makes the statement false.

Isometric Drawing

A drawing of a three-dimensional object shows a corner view of a figure.

Orthographic Drawing

The top view, front view and right-side view of a three-dimensional figure.

Foundation Drawing

A drawing that shows the base of a structure and the height of each part

Net

A two-dimensional pattern that you can fold to form a three-dimensional figure.

Point

A location.

Space

The set of all points.

Line

A series of points that extend in two directions without end.

Collinear Points

Points that lay on the same line.

Plane

A flat surface that has no thickness. Contains many lines and extends without end in the directions of its lines.

Coplanar

Figures in the same plane.

Postulate

An accepted statement of fact.

Axiom

An accepted state of fact.

Postulate 1.1 "Through any two points..."

Through any two points there is exactly one line.

Postulate 1.2 "If two lines intersect..."

If two lines intersect, then they intersect at exactly one point.

Postulate 1.3 "If two planes intersect..."

If two planes intersect, then they intersect in exactly one line.

Postulate 1.4 "Through any three..."

Through any three noncollinear points there is exactly one plane.

Segment

The part of a line consisting of two points, called endpoints and all the points between them.

Ray

The part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.

Opposite Rays

Collinear rays with the same endpoint. They form a line.

Parallel Lines

Lines that lie in the same plane and do not intersect.

Skew Lines

Lines that do not lie in the same plane.

Parallel Planes

Planes that do not intersect

Ruler Postulate

The points of a line can be put into a one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.

Coordinate

The distance and direction from the origin of a number line. The coordinates of a point on a coordinate plane are in the form where x is the x-coordinate and y is the y-coordinate.

Congruent Segments

Segments that have the same length.

Segment Addition Postulate

If three points, A, B, and C are collinear and B is between A and C, then AB + BC = AC.

Midpoint

A point that divides the segment into two congruent segments.

Protractor Postulate

Let ray OA and ray OB be opposite rays in a plane. Ray OA, ray OB, and all rays with endpoint O that can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 so that:

a. ray OA is paired with 0 and ray OB is paired with 180.

b. If ray OC is paired with x and ray ODis paired with y, then the measure of angle COD = |x-y|.

a. ray OA is paired with 0 and ray OB is paired with 180.

b. If ray OC is paired with x and ray ODis paired with y, then the measure of angle COD = |x-y|.

Angle

Formed by two rays with the same endpoint. The rays are the sides of the angle and with the common endpoint is the vertex of the angle.

Acute Angle

An angle whose measure is between 0 and 90

Right Angle

An angle whose measure is 90.

Obtuse Angle

An angle whose measure is between 90 and 180.

Straight Angle

An angle whose measure is 180.

Congruent Angles

Angles that have the same measure

Vertical Angles

Two angles whose sides form two pairs of opposite rays.

Adjacent Angles

Two coplanar angles that have a common side and a common vertex but no common interior points

Complementary Angles

Two angles whose sum equals 90

Supplementary Angles

Two angles whose sums equal 180.

Construction

A geometric figure made with only a straightedge and a compass.

Straightedge

A ruler with no markings on it.

Compass

A geometric tool used to draw circles and parts of circles, called arcs.

Perpendicular Lines

Lines that intersect and form right angles.

Perpendicular Bisector

A line, segment, or ray that is perpendicular to the segment at its midpoint.

Angle Bisector

A ray that divides an angle into two congruent angles.