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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