Geometry Final Study Guide: Key Concepts, Theorems, and Formulas

Point

A location in space

Line

A straight path with no thickness that extends forever in both directions

Plane

A flat surface that extends infinitely in all directions

Segment

Part of a line with two endpoints

Ray

A part of a line that starts at one point and extends forever in one direction

Angle

Formed by two rays with a common endpoint (vertex)

Congruent

Equal in measure

Bisect

To divide into two equal parts

Midpoint

The point that divides a segment into two equal parts

Perpendicular

Lines that intersect to form right angles

Parallel

Lines in the same plane that never intersect

Triangle Sum Theorem

The sum of the interior angles of a triangle is 180°

Exterior Angle Theorem

An exterior angle is equal to the sum of the two remote interior angles

Equilateral Triangle

3 equal sides

Isosceles Triangle

2 equal sides

Scalene Triangle

No equal sides

Acute Triangle

All angles < 90°

Right Triangle

One angle = 90°

Obtuse Triangle

One angle > 90°

SSS

Side-Side-Side

SAS

Side-Angle-Side

ASA

Angle-Side-Angle

AAS

Angle-Angle-Side

HL

Hypotenuse-Leg (for right triangles only)

Parallelogram

Opposite sides are parallel and congruent

Rectangle

Parallelogram with 4 right angles

Rhombus

Parallelogram with 4 equal sides

Square

Rectangle + Rhombus

Trapezoid

One pair of parallel sides

Isosceles Trapezoid

Trapezoid with congruent legs

Radius

Distance from center to edge

Diameter

Distance across the circle through the center (2 × radius)

Chord

A segment with both endpoints on the circle

Tangent

A line that touches the circle at exactly one point

Arc

A portion of the circumference

Central Angle

Angle with vertex at the center

Inscribed Angle

Angle with vertex on the circle

Translation

Slide

Reflection

Flip

Rotation

Turn

Dilation

Resize (enlargement or reduction)

Distance Formula

√[(x₂ − x₁)² + (y₂ − y₁)²]

Midpoint Formula

((x₁ + x₂)/2 , (y₁ + y₂)/2)

Slope Formula

(y₂ − y₁) / (x₂ − x₁)

Area of Triangle

½ × base × height

Area of Rectangle

base × height

Area of Trapezoid

½ × (base₁ + base₂) × height

Area of Circle

π × r²

Volume of Rectangular Prism

length × width × height

Volume of Cylinder

π × r² × height

Volume of Sphere

(4/3) × π × r³

Volume of Cone

(1/3) × π × r² × height

Volume of Pyramid

(1/3) × base area × height