Geometry Properties of Equality and Congruence

Symmetric Property

If AB = CD, then CD = AB.

Transitive Property

If AB = DC and DC = XY, then AB = XY.

Addition Property of Equality

If AB = MN, then AB + EF = MN + EF.

Subtraction Property of Equality

If AB + BC = BC + EF, then AB = EF.

Multiplication Property of Equality

If AB = XZ, then 2AB = 2XZ

Division Property of Equality

If 2(XY) = 50, then XY = 25.

Distributive Property

a(b + c) = ab + ac

a(b - c) = ab - ac

Complementary angles

Two angles whose sum is 90 degrees

Supplementary angles

Two angles whose sum is 180 degrees

Right angle

an angle that measures 90 degrees

Straight angle

an angle that measures 180 degrees

Vertical angles

A pair of opposite congruent angles formed by intersecting lines

Hypothesis

IF CLASS IS CANCELED, then I get to leave.

Conclusion

If class is canceled, THEN I GET TO LEAVE.

Postulate

a statement that is accepted as true without proof

Midpoint

A point that divides a segment into two congruent segments

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Segment bisector

a segment, ray, line, or plane that intersects a segment at its midpoint

Angle Addition Postulate

if point B lies in the interior of

Congruent segments

segments that have the same length

Theorem

A statement that has been proven

Angle bisector

a ray that divides an angle into two congruent angles

Vertical Angles Theorem

Vertical angles are congruent

Congruent angles

angles that have the same measure

Midpoint Theorem

If M is the midpoint of AB, then AM=1/2AB and MB=1/2AB

Angle Bisector Theorem

If ray BX is the bisector of

perpendicular lines

Lines that intersect to form right angles

Perpendicular Lines form

congruent adjacent angles

If two lines form congruent adjacent angles

the lines are perpendicular lines

If the exterior sides of two adjacent acute angles are perpendicular

then the angles are complementary