Geo Chapter 2: Deductive Reasoning

Subtraction Property of Equality

If a=b and c=d, then a-c = b-d.

Reflexive Property

A figure is congruent to itself

Substitution Property

If a = b, then a or b may be substituted for the other in any equation or inequality

Symmetric Property

If a = b, then b = a.

Definition of a bisector

A bisector cuts a figure into two (smaller) congruent figures.

Midpoint Theorem

If M is the midpoint of segment AB, then AM = ½AB and MB = ½AB

Conditional statement are also called...

if-then statements.

If-then statements are also called...

conditional statements.

In the logical statement p→q, p represents the...

hypothesis.

In the logical statement p→q, q represents the...

conclusion.

The converse of a statement is formed by...

interchanging the hypothesis and the conclusion.

To prove a statement is false, you can provide a...

counterexample.

If a conditional statement and its converse are both true, then it is called a...

biconditional.

A biconditional statement contains the phrase...

"if and only if"

The statement
"p if and only if q"
is an example of a...

biconditional statement

Addition Property of Equality

If a=b and c=d, then a+c = b+d.

Multiplication Property of Equality

If a=b, then ca = cb

Division Property of Equality

If a=b and c≠0, then ca = cb

Transitive Property

If a=b and b=c, then a=c
or
If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C

Definition of a midpoint

If M the midpoint of AB, then AM=MB

Angle Bisector Theorem

If ray BX is the bisector of ∠ABC, then m∠ABX=½m∠ABC and m∠XBC=½m∠ABC

Definition of Vertical Angles

Two angles such that the sides of one angle are opposite rays to the sides of the other angle.

Vertical Angle Theorem

Vertical angles are congruent

Perpendicular lines

Lines that intersect to form right angles

If two lines are perpendicular, then they form...

congruent adjacent angles.

If two lines form congrent adjacent angles, then the lines...

are perpendicular.

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are...

complementary.

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

are congruent

If two angles are complements to the same angles (or two congruent angles), then the two angles...

are congruent.