GEOMETRY

Inductive Reasoning: the study of patterns

Deduction Reasoning: the study of events that lead up to a proof or examining the reasons why something happens. This is reasoning is used for proofs.

Coplanar lines: Lines that are on the same plane.

Congruent: When a segment is bisected ( perfectly in the center), it’s halved are congruent.

Complimentary Angles are two angles who’s measures add up to 90°

( Imagine the angles pictured)

m90°

Supplementary angles are two angles whose measures add up to 180°

m4 Different Ways to State a Theorem

If -Then Statments: if p then q: ” If I am good, then I hold the monkey.”

Converse Statements: (switch) if q then p: “If I hold the monkey then I am good.”

These 2 are “statement forms”

You can negate the statement

Inverse Statements: If not p then not q. “If I’m not good. then I won’t hold the monkey.”

Reverse and Negate the Statement:

Contrapositive: If not q, then not p. “If I don’t hold the monkey, then I’m not good.”

See how these statements apply to theorems.

If the statement is true, then the contrapositive is also logically true. There are four ways to state theorems. When a statement and it’s converse are true, all four statements are true.

Summary of If-then Statements

• statement

• inverse

• converse

• contrapositive

Together the make the

BICONDITIONAL STATEMENT
P if and only if q

“if two lines intersect, then they intersect at a unique point”

The Biconditional of that statement is:

Two lines intersect if and only if they intersect at a unique point.

ANGLES

An angle is two rays that share the same endpoint.

Angles and their Theorems

Algebraic Properties

The Reflective Property: when a value is equal to itself ( i.e. a mirror image)

Reflexive Property: when an angle or segment is congruent to itself.

Substitution Property

Let’s say we have two statements:

m<1+m<3= 180

m<1= m<2

Using the substitution property, we can switch two angles that are equal.

The measure of angle 1 and the measure of angle 2 on our first statement.

m<1+m<3= 180

m<1= m<2

So the measure of angle 2 plus the measure of angle three equal 180

m<2+m<3= 180

Switching the values of the measure angle 1 and the measure 2 is substitution.

Transitive Property

A=B as B=C the A=C

Angle Related Theorems

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