What definitions properties postulates and theorems you need to know for this geometry unit

Right angle

An angle that measures exactly 90 degrees.

Straight angle

An angle that measures exactly 180 degrees.

Perpendicular lines

Lines that intersect to form right angles.

Midpoint

The point that divides a segment into two congruent segments.

Segment bisector

A point, line, or segment that divides another segment into two equal parts.

Angle bisector

A ray that divides an angle into two congruent angles.

Perpendicular bisector

intersect to form right angles

Congruent circles

Circles that have the same radius.

Congruent segments

Segments that have the same length.

Congruent angles

Angles that have the same measure.

Congruent triangles

Triangles that are the same size and shape.

Parallel lines

Lines in a plane that do not intersect and are equidistant from each other.

Coinciding lines

Lines that lie on top of each other; they have all points in common.

Supplementary angles

Two angles whose measures add up to 180 degrees.

Complementary angles

Two angles whose measures add up to 90 degrees.

Linear pair

A pair of adjacent angles that form a straight angle.

APOE

addittion

SPOE

subtraction

MPOE

multipication

DPOE

division

Distributive property

a(b + c) = ab + ac.

Combine like terms

To simplify an expression by merging terms that have the same variable raised to the same power.

Substitution

A property that allows one to replace an expression with another expression that is equal.

Reflexive property of congruence or equality

A quantity is congruent or equal to itself.

Symmetric property of congruence or equality

If a = b, then b = a.

Transitive property of equality

If a = b and b = c, then a = c.

Segment addition postulate

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

Angle addition postulate

If point B is in the interior of angle AOC, then the measure of angle AOB + the measure of angle BOC = the measure of angle AOC.

Right angles theorem

All right angles are congruent.

Perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Vertical angles theorem

Vertical angles are congruent.

Linear pair theorem

If two angles form a linear pair, then they are supplementary.

Congruent complements theorem

If two angles are complementary to the same angle, then they are congruent.

Congruent supplementary theorem

If two angles are supplementary to the same angle, then they are congruent.

Midpoint theorem

The midpoint of a segment is equidistant from the endpoints.

Segment bisector theorem

A segment bisector divides a segment into two congruent segments.

Angle bisector theorem

An angle bisector divides an angle into two congruent angles.