Geometry: Postulates, Theorems, and Proofs (Page 1 Notes)

Vocabulary flashcards covering key postulates, theorems, properties, and concepts from Page 1 notes on geometry proofs.

Midpoint

A point M on segment AB such that AM = MB (A, M, B are collinear).

Midpoint Theorem

If M is the midpoint of AB, then AM = MB and A, M, B are collinear.

Reflexive Property

A quantity is equal to itself: a = a; congruence a ≅ a.

Segment Addition Postulate

If B lies between A and C on a line, then AB + BC = AC.

Supplementary Angles

Two angles whose measures add to 180°.

Supplement Theorem

Two angles that form a linear pair are supplementary.

Symmetric Property (Equality/Congruence)

If a = b, then b = a; If AB ≅ BC, then BC ≅ AB.

Angle Addition Postulate

The measure of an angle formed by two adjacent angles equals the sum of the two measures: m∠ABC + m∠CBD = m∠ABD.

Complementary Angles

Two angles whose measures add to 90°.

Complement Theorem

If two angles form a right angle, then they are complementary.

Transitive Property

If a = b and b = c, then a = c (and similarly for congruence).

Congruent Segments

Segments that have equal length: AB ≅ BC if and only if AB = BC.

Congruent Supplements

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

Addition Property of Equality

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

Congruent Angles

Angles that have equal measures: ∠A ≅ ∠B iff m∠A = m∠B.

Congruent Complements

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

Subtraction Property of Equality

If a = b, then a − c = b − c.

Vertical Angles

Two nonadjacent angles formed by intersecting lines.

Vertical Angles Theorem

Vertical angles are congruent.

Multiplication Property

If a = b, then ac = bc.

Right Angle

An angle with measure 90°.

All Right Angles Are Congruent

All right angles are congruent to each other.

Division Property

If a = b, then a/c = b/c (c ≠ 0).

Linear Pair

Two adjacent angles whose non-common sides are opposite rays.

Perpendicular Lines Form 4 Right Angles

If two lines are perpendicular, they intersect to create four right angles.

Substitution

If a = b, then a can be substituted for b in any expression.

Segment Bisector

A segment, line, or plane that intersects a segment at its midpoint.

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

If two triangles are congruent, then their corresponding parts are congruent.

Distributive Property

a(b + c) = ab + ac.

Angle Bisector

A ray that divides an angle into two congruent angles.

Reasons for Proofs

The justifications used to explain each statement in a geometric proof.