Unit 1 Transformations and Congruence

Line

It has no thickness and it continues forever in both directions.

Line Segment

A portion of a line with two end points.

Opposite Rays

Rays with the same initial point that extend in opposite directions.

Midpoint

The point that bisects a segment. (Divides into two segments of equal length.)

Bisect

To divide something into 2 equal parts.

Perpendicular Lines

Two lines which intersect at a right angle (90 degrees).

Parallel Lines

Two lines which exist in the same plane but will never intersect.

Postulate

Something assumed as true as the basis for further reasoning, discussion, or proofs.

Midpoint Formula

Acute Angle

An angle that measures more than zero degrees but less than 90 degrees.

Obtuse Angle

An angle with measure greater than 90 degrees but less than 180 degrees.

Straight Angle

An angle with measure of 180 degrees.

Right Angle

An angle with measure of 90 degrees.

Protractor

Tool used to measure angles

Collinear Points

Points lying on the same line

Supplementary Angles

Two angle measures with a sum of 180 degrees.

Complimentary Angles

Two angles with a sum of 90 degrees.

≅

Congruent

=

Equal

Congruent

Having the same size and shape

Linear Pair

Two adjacent angles that form a straight line

Angle

A figure formed by with two rays with a common endpoint.

Degree

Unit of measurement for an angle

Angle Bisector

a line or ray that divides an angle into two congruent angles

Vertex

The common endpoint of an angle

Endpoint

the point where a ray begins or the points that define a segment

Construction

a geometric drawing that uses a limited set of tools, usually a compass and a ruler

Exterior

all points not on the angle or in its interior

Interior

all points not on the sides of an angle but within the its sides

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Angle Addition Postulate

for any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts

Vertical angles

two angles whose sides form two pairs of opposite rays

Vertical Angle Theorem

Vertical angles are always congruent

Non-rigid motion

Does not maintain shape and/or size

Point

An undefined term in geometry, it names a location and has no size.

Preimage

The original figure in a transformation.

Ray

A part of a line that starts at an endpoint and extends forever in one direction.

Reflection

A transformation across a line, called the line of reflection, such that the line of reflection is the perpendicular bisector of each segment joining each point and its image.

Rigid motion

A transformation that does not change the size or shape of a figure.

Rotation

A transformation about a point P, also known as the center of rotation, such that each point and its image are the same distance from P. All of the angles with vertex P formed by a point and its image are congruent.

Segment

A part of a line consisting of two endpoints and all points between them.

Theorem

A statement that has been proven.

Transformation

A change in the position, size, or shape of a figure or graph.

Translation

A transformation that shifts or slides every point of a figure or graph the same distance in the same direction.

Plane

a flat surface that has no thickness and extends forever

Coplanar

of the same plane

Dilation

A transformation that changes the size of an object, but not the shape.