geomatry simplfied terms study guide

Point

An undefined term in geometry.

Line

An undefined term in geometry.

Plane

An undefined term in geometry.

Postulate

A statement accepted as true without proof.

Midpoint

A point that divides a segment into two equal parts.

Distance Formula

The formula for distance between 2 points (x₁, y₁) and (x₂, y₂) is \sqrt{(x₂-x₁)^2 + (y₂-y₁)^2}.

Midpoint Formula

The formula is \left(\frac{x₁+x₂}{2}, \frac{y₁+y₂}{2}\right).

Complementary Angles

Two angles that add up to 90°.

Supplementary Angles

Two angles that add up to 180°.

Vertical Angles

Opposite angles formed by two intersecting lines; always congruent.

Area of Triangle

The formula for area is ½ × base × height.

Circumference of Circle

The formula is 2πr.

Inductive Reasoning

Using patterns and examples to form a guess.

Conjecture

A guess based on inductive reasoning.

Counterexample

One example that proves a conjecture false.

Deductive Reasoning

Using facts and logic to make a conclusion.

Conditional Statement

An 'If p, then q' statement.

Converse

Switch the hypothesis and conclusion.

Inverse

Negate both the hypothesis and conclusion.

Contrapositive

Switch and negate both parts.

Biconditional

A statement that's true both ways, written 'if and only if.'

Law of Detachment

If p → q is true and p is true, then q is true.

Law of Syllogism

If p → q and q → r are true, then p → r is true.

Proof

A logical argument using facts, definitions, and theorems to show a statement is true.

Property of Equality

A rule that states quantities stay equal when you do the same thing to both sides.

Distributive Property

The property states a(b + c) = ab + ac.

Subtraction Property of Equality

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

Addition Property of Equality

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

Multiplication Property of Equality

If a = b, then ac = bc.

Division Property of Equality

If a = b and c ≠ 0, then a/c = b/c.

Theorem

A statement that can be proven true.

Postulate (Axiom)

A basic statement accepted as true without proof.

Definition in Geometry

A statement that describes a geometric concept and is always reversible.

Two-Column Proof

A proof format with statements on one side and justifications on the other.

Flowchart Proof

A proof using boxes and arrows to show the logical order.

Paragraph Proof

A proof written as a logical paragraph explaining reasoning.

Congruent Supplements Theorem

If two angles are supplementary to the same angle, they are congruent.

Congruent Complements Theorem

If two angles are complementary to the same angle, they are congruent.

Vertical Angles Theorem

Vertical angles are always congruent.