Chapter 2 Geometry properties

If <1 and <2 are right angles, then...

<1 is congruent to <2.

If <1 and <2 are complementary and <2 and <3 are complementary, then...

<1 is congruent to <3.

If <A and <B form a linear pair, then...

<A and <B are supplementary.

Simplify

A justification that completes an operation. This is used often as a reason to give a result to an operation.

Definition: Linear pair

A pair of adjacent angles formed when two lines intersect.

Paragraph Proof

A style of proof in which the statements and reasons are presented in paragraph form.

Two column proof

A type of proof that has numbered statements and corresponding reasons that show an argument in a logical order. Presented in 2-6.

Right Angle Congruence Theorem

All right angles are congruent.

Theorem

Any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs.

Multiplication POE

If a = b, then ac = bc

Congruent Complements Theorem

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

Linear Pair Theorem

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

Q.E.D

Initials for the Latin phrase "quod erat demonstratum" which stands for "that which has been demonstrated". This indicates when an author is done with a proof. This also may be indicated with a symbol that looks like a filled in rectangle or "tombstone".

When writing a proof, it is important to _____ each logical step with a reason.

Justify. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them.

Writing Justifications

Write a justification (reason) for each step. Each statement (step) in a problem has a reason that you are providing.

When writing a geometric proof...

You use deductive reasoning to create a chain of logical steps that move from the hypothesis to the conclusion of the conjecture you are proving. By proving that the conclusion is true, you have proven that the original conjecture is true.

Reflexive POE

a = a

Flow Chart Proof

a graphic representation using symbols interconnected with line segments or rays, of the successive steps, in a procedure or system

Distributive POE

a(b+c)=ab+ac a(b-c)=ab-ac

Transitive POE

if a = b and b= c, then a = c

Division POE

if a = b and c =/ 0, then a/c = b/c

Addition Property Of Equality (POE)

if a = b, then a + c = b + c

Subtraction POE

if a = b, then a - c = b - c

Symmetric POE

if a = b, then b = a

Substitution POE

if a = b, then b can be substituted for a in any expression.