Geometry regents review

Point

A location named with a capital letter

Line

One dimensional. Goes on forever in both directions.

Segment

A measurable part of a line that consists of two endpoints and all the points between them

Ray

A line with one endpoint and goes on forever in one direction

Collinear

Points on the same line

Plane

Two dimensional,goes on forever in all directions

Coplanar

Points on the same plane

Circle

The path of of all points that are equaldistant from a point called the center

Radius

A segment connecting the center of the circle to any point on the circle

Postulate

Considered true without proof

Angle

The union of two non-collinear rays with the same endpoint

Convex

An angle that is 180 degrees or less

Nonconvex

An angle greater than 180 but less than 360

Angle bisector

A ray that divides an angle into two equal angles

Segment bisector

A segment, line or ray that divides a segment into two equal segments

Degree

1/360 of a circle

Zero angle

A ray that equals 0 degrees

Straight angle

A line that measures 180 degrees

Midpoint

A point that is halfway between the endpoints of a segment

Right angle

An angle that measures 90 degrees

Purpendicular

When two lines, segments or rays intersect forming a 90 degree angle

Equidistant

A point that is an equal distance from two or more things

Circumcenter

Where all the perpendicular bisectors of a triangle intersect

Complimentary

The sum of two angles that equal 90

Supplementary

Sum of two angles that equal 180

Adjacent

Next to

Median of a triangle

A segment whose endpoints are a vertex of the triangle and midpoint of the opposite side

Centroid

Where the midpoints of a triangle intersect

Altitude of a triangle

Perpendicular line from the vertex of the triangle to the opposite side. Must create a right angle

Orthocenter

Where the altitudes of the triangle meet

Incenter

Where the angle bisectors of a triangle meet

PBC/ABI/MC/AO

Perpendicular bisectors,circumcenter/angle bisectors, incenter/medians, centroid/altitudes,orthocenter

Axioms

Proof

Theorem

Logical consequence of axioms

Auxiliary line

Added lines to help solve a problem

Rotation

Need to know: need to translate point of rotation to (0,0) before rotating. Degree of rotation.

Translation

Need to know: same shape and size. Direction. Distance.

Reflection

Need to know: stays same shape and size. Reflection line

R90 degrees

(X, Y) → (-Y, X)

Rotation 180 degrees

(X, Y) → (-X,-Y)

R270 degrees

(X,Y)→(Y,-X)