Geometry Ch 2 Reasoning & Proof

Counterexample

a specific case for which the conjecture (or statement) is false

Perpendicular lines

two lines that intersect to form right angles

Converse Statement

the hypothesis and the conclusion of a conditional statement are switched

Inverse Statement

A conditional statement that negates the hypothesis and negates the conclusion.

vertical angles

A pair of opposite congruent angles formed by intersecting lines

linear pair

a pair of adjacent angles that form a line, have a sum of 180 degrees

Reflexive

a=a

Symmetric

if a=b, then b=a

Transitive

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

complementary angles

Angles with a sum of 90 degrees

supplementary angles

Angles with a sum of 180 degrees

addition property

If a = b, then a + c = b + c

subtraction property

If a = b, then a - c = b - c

multiplication property

If a = b, then a·c = b·c

division property

if a = b and c is not equal to 0, then a/c = b/c

distributive property

a(b+c)=a·b+a·c

substitution property

If a=b, then b can replace a in any expression

Definition of Midpoint

A point that divides a segment into two congruent segments

Definition of right angles

angles that equal 90 degrees

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.