MATH THEOREMS

Right angles congruent

Right angles congruent

If two angles are right angles, then they are congruent.

Straight angles congruent

If two angles are straight angles, then they are congruent.

Relationships w conditional and contrapositive

If a conditional statement is true, then the contrapositive of the statement is also true. (If p, then qIf ~q, then ~p.)

Supplementary to same angle

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

Supplementary to congruent angles

If angles are supplementary to congruent angles, then they are congruent.

Complementary to same angle

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

Complementary to congruent angles

If angles are complementary to congruent angles, then they are congruent.

Addition property 1 seg + 2 congruent

If a segment is added to two congruent segments, the sums are congruent.

Addition property 1 angle + 2 congruent angle

If an angle is added to two congruent angles, the sums are congruent.

Addition property congruent segs + congruent segs

If congruent segments are added to congruent segments, the sums are congruent.

Addition property congruent angles + congruent angles

If congruent angles are added to congruent angles, the sums are congruent. (Addition Property)

Subtraction property seg - congruent segs

If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent.

Subtraction property congruent segs - congruent segs

If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent.

Multiplication property segs/angles congruent

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

Division property segs/angles congrurent

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

Transitive property angles/segs are congruent to same

If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other.

Transitive property angles/segs congruent to congruent angles/segs

If angles (or segments) are congruent to congruent angles (or segments), they congruent to each other.

VAT

Vertical angles are congruent.

Radii of a circle are…

All radii of a circle are congruent.

ITT

If two sides of a triangle are congruent, the angles opposite the sides are congruent. (If A. then A.)

ITT-C

If two angles of a triangle are congruent, the sides opposite the angles are congruent. (If A, then A.)

Midpoint formula

X1+x2/2, y1+y2/2

RAT

If two angles are both supplementary and congruent, then they are right angles.

EDT

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

EDT-C

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

def parallel

If two nonvertical lines are parallel, then their slopes are equal.

converse def parallel

If the slopes of two nonvertical lines are equal, then the lines are parallel.

Slope relationship w perp lines

If two lines are perpendicular and neither is vertical, each line’s slope is the opposite reciprocal of the other’s.

Converse slope relationships w perp lines

If a line’s slope is the opposite reciprocal of another line’s slope, the two lines perpendicular.

EAT

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

Alternate Interior

If two lines are cut by a transversal such that two alternate interior angles are congruent, the lines are parallel. (Alt. int. /is s|| lines)

Alternate exterior

If two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel. (Alt. ext. Z.s =^|| lines)

Corresponding

If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel. (Corr. Z.s s^|| lines)

Same-side interior (supp)

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.

Same-side exterior (supp)

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.

2 coplaner lines perp to 3rd line

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

parallel postulate alt interior

If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent. (|| lines ^alt. int. Z.s s)

parallel postulate

If two parallel lines are cut by a transversal, then any pair of the angles formed are either congruent or supplementary.

parallel postulate alt ext congruent

If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent. (|| lines ^alt. ext. Z.s =)

parallel postulate corresponding congruent

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent. (|] lines corr. Z.s =)

parallel postulate same side int supp

If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.

parallel postulate same side ext supp

If two parallel lines are cut by a transversal, each pair of exterior angles on the same side of the transversal are supplementary.

If a line is perp to one of two parallel lines…

In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other.

T.P (parallel)

If two lines are parallel to a third line, they are parallel to each other.

quadrilateral

a four sided polygon

parallelogram

a quadrilateral in which both pairs of opposite sides are parallel

rectangle

a parallelogram in which at least one angle is a right angle

rhombus

a parallelogram in which at least two sides are congruent

kite

a quadrilateral in which two disjoint pairs of consecutive sides are congruent

square

a parallelogram that is both a rectangle and rhombus

trapezoid

a quadrilateral with exactly one pair of parallel sides. parallel sides are called bases of the trapezoid

isosceles trapezoid

a trapezoid in which nonparallel sides (legs) are congruent