Honors Geometry Theorems

Theorem 1

If two angles are right angles, then they are congruent

Theorem 2

If two angles are straight angles then they are congruent

Addition Property

If a segment (or angle) is added to two congruent segments (or angles), then the sums are congruent

Addition Property

If congruent segments (or angle) are added to congruent segments (or angle), then the sums are congruent

Subtraction Property

If a segment (or angle) is subtracted to two congruent segments (or angles), then the differences are congruent

Subtraction Property

If congruent segments (or angles) are subtracted to congruent segments (or angles), then the differences are congruent

Multiplication Property

If segments (or angles) are congruent, then their like multiples are congruent

Division Property

If segments (or angles) are congruent, then their like divisions are congruent.

CPCTC

corresponding parts of congruent triangles are congruent

ITT (isosceles triangle theorem)

if two sides of a triangle are congruent, then the angles opposite the sides are congruent

ITTC (isosceles triangle theorem converse)

if two angles of a triangle are congruent, then the sides opposite the angles are congruent

RAT (right angle theorem)

if two congruent angles are supplementary to each other, they are right angles

EDT

if two points are each equidistant from the endpoints of a segment, then the points determine the perpendicular bisector

CEDT

if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment

EAT

the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle

Parallel Lines

if two lines are cut by a transversal such that two alternate interior angles are congruent, the lines are parallel

Parallel Lines

if two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel

Parallel Lines

if two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel

Parallel Lines

if two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, the lines are parallel

Parallel Lines

if two lines are cut by a transversal such that two exterior angles on the same side of the transversal are supplementary, the lines are parallel

Parallel Lines

if two coplanar lines are perpendicular to a third line, they are parallel

Proving a Quadrilateral is a Parallelogram 1

If both pairs of opposite sides of a quadrilateral are parallel then the quadrilateral is a parallelogram

Proving a Quadrilateral is a Parallelogram 2

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Proving a Quadrilateral is a Parallelogram 3

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram

Proving a Quadrilateral is a Parallelogram 4

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Proving a Quadrilateral is a Parallelogram 5

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Congruent Chords

If 2 chords are equidistant from the center of a circle, they are congruent

Congruent Chords

If 2 chords are congruent, they are equidistant from the center of the circle

Perp. Bis. Circles

If a radius is perpendicular to a chord, then the radius bisects the chord

Perp. Bis. Circles

If a radius bis. a chord, it is also perp. to the chord

Perp. Bis. Circles

The perp. bis. of a chord passes through the center of a circle