Geometry Key Terms: Midpoints, Congruent Segments, Angles, and Postulates

Midpoint

A point that divides a segment into two congruent segments.

Congruent

Same size, Same shape.

Congruent segments

Segments with the same length

Congruent Angles

Angles with the same measure

Collinear

Points that lie on the same line

Non-Collinear

Points that do not lie on the same line

Coplaner

Points on the same plane.

Non-coplaner

Points that do not lie on the same plane.

Between

If A, B, C are distinct points and B is on segment AC, then B is between AC.

Segment

A part of a line with 2 endpoints and all points in between.

Adjacent Angles

Angles that share a common side and vertex, but no common interior points.

Linear pair

Two adjacent angles with uncommon sides that form a line.

Angle Bisector

A ray in the interior of an angle that forms 2 congruent angles.

Postulate

A statement accepted as true without proof

Theorem

A proven statement.

Line postulate

Through any 2 points there is exactly one line.

Parallel Postulate

Through a point not on a line, there is exactly a line parallel to the given line.

Perpendicular Postulate

Through a point not on a line, there is exactly one line perpendicular to the given line.

Linear-Pair postulate

If 2 angles form a linear pair, then they are supplementary.

Segment Addition Postulate

If point B is collinear with and between points A and C, then AB+BC=AC

Angle addition postulate

If point D is in the interior of ∠ABC + m∠DBC = m∠ABC

Reflexive Property

a=a

Transitive Property

If a=b and b=c then a=c

Substitution Property

If a=b, then b can be replaced with a and vice-versa. If a=bc+d, then bc+d can replace a.

Distribution Property

a(b+c) = ab+ac

Addition Property

If a=b, then a+c = b+c. If a=b, and c=d, then a+c=b+d. If a+a = b then 2a=b

Subtraction Property

If a=b, then a-c = b-c. If a=b, c=d, then a-c=b-d. If 2a-a=b then a=b

Multiplication Property

If a=b, then ac=bc. If a=b, and c=d then ac=bd. If a(a) = b then a^2 = b

Division Property

If a=b, then a/c = b/c. If a=b and c=d then a/c = b/d. If a^2/a = b then a=b