Accel Geometry Quiz 3-1 to 3-3 Review

Definition of a Right Angle

An angle is a right angle if and only if it equals 90 degrees

Definition of Midpoint

If M is the midpoint of segment AB, then segment AM is congruent to segment MB

Definition of Angle Bisector

a ray that divides an angle into 2 congruent angles

Vertical Angles are Congruent

Segment Addition Postulate

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

Angle Addition Postulate

If P is in the interior of

Definition of Segment Bisector

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

Definition of linear pair

two adjacent, supplementary angles (that form a line)

Definition of Complementary Angles

Two angles are complementary if their sum is 90 degrees

Definition of Supplementary Angles

Two angles whose sum is 180 degrees

Definition of Perpendicular Lines

Two lines that intersect to form right angles

Vertical Angles Theorem

Vertical angles are congruent

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equal.

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal.

Multiplication Property of Equality

If you multiply each side of an equation by the same nonzero number, the two sides remain equal.

Division Property of Equality

If you divide each side of an equation by the same nonzero number, the two sides remain equal.

Substitution Property of Equality

If a=b, then a may be replaced by b in any equation or expression

Distributive Property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

Reflexive Property of Equality

a=a, AB=AB, m

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

If a = b and b = c, then a = c

Definition of congruent angles

Two angles are congruent if and only if they are equal

Definition of congruent segments

Two segments are congruent if and only if they have the same length.

Congruent Complements Theorem

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

Congruent Supplements Theorem

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

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Definition of Perpendicular Lines

2 lines that intersect to form a right angle

Transitive Property of Congruence

If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF

Symmetric Property of Congruence

If segment AB is congruent to segment CD, then segment CD is congruent to segment AB

Reflexive Property of Congruence

segment AB is congruent to segment AB

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Converse of the Corresponding Angles Postulate

If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Converse of the Alternate Interior Angles Theorem

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Converse of Alternate Exterior Angles Theorem

If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Converse of Consecutive Interior Angles Theorem

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

If two lines are parallel to the same line....

then they are parallel to each other