GEOMETRY REVIEW

Point

Basic unit of geometry with no size or dimension.

Line

Straight one-dimensional figure that extends infinitely in both directions.

Plane

Flat, two-dimensional surface that extends infinitely in two directions.

Angle

Formed by two rays with a common endpoint.

Acute Angle

An angle that is less than 90°.

Right Angle

An angle that is exactly 90°.

Obtuse Angle

An angle that is greater than 90° but less than 180°.

Straight Angle

An angle that is exactly 180°.

Parallel Lines

Lines that never intersect and are equidistant.

Perpendicular Lines

Lines that intersect at right angles.

Equilateral Triangle

A triangle with three equal sides and angles.

Isosceles Triangle

A triangle with two equal sides and angles.

Scalene Triangle

A triangle with no equal sides or angles.

Right Triangle

A triangle with one angle that is 90°.

Triangle Properties

The sum of angles in a triangle equals 180°.

Pythagorean Theorem

In a right triangle, $a^2 + b^2 = c^2$.

Quadrilateral

A polygon with four sides; types include Parallelograms, Rectangles, Rhombuses, and Squares.

Area of Triangle

Given by the formula: $Area = \frac{1}{2} \times base \times height$.

Area of Rectangle

Calculated as: $Area = length \times width$.

Area of Circle

Determined by the formula: $Area = \text{π} r^2$.

Circumference of Circle

Calculated using: $Circumference = 2\text{π} r$.

Volume of Prism

Given by the formula: $Volume = Base \times height$.

Volume of Cylinder

Calculated as: $Volume = \text{π} r^2 h$.

Surface Area of Cylinder

Given by: $Surface Area = 2\text{π} r(h + r)$.

Volume of Sphere

Given by the formula: $Volume = \frac{4}{3}\text{π} r^3$.

Surface Area of Sphere

Calculated as: $Surface Area = 4\text{π} r^2$.

Translation

Sliding a shape without rotation or flipping.

Rotation

Turning a shape around a fixed point.

Reflection

Flipping a shape over a line to create a mirror image.

Dilation

Resizing a shape while maintaining its proportions.

Congruence

Property preserved under transformations.

Similarity

Relationship indicating that shapes are proportionally scaled.

Triangle Similarity - AA

Two angles in one triangle are equal to two angles in another triangle.

Triangle Similarity - SSS

The corresponding sides of two triangles are in proportion.

Triangle Similarity - SAS

Two sides are in proportion, and the included angle is equal.

Distance Formula

$d = \text{√}((x_2 - x_1)^2 + (y_2 - y_1)^2)$.

Midpoint Formula

$M = \text{(}\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\text{)}$.

Slope

Calculated using: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Sine

Ratio of the opposite side to the hypotenuse in a right triangle.

Cosine

Ratio of the adjacent side to the hypotenuse in a right triangle.

Tangent

Ratio of the opposite side to the adjacent side in a right triangle.

SOH-CAH-TOA

Mnemonic for sine, cosine, and tangent definitions.

Arc

A portion of a circle defined by two endpoints.

Chord

A line segment whose endpoints lie on the circle.

Tangent (Line)

A line that touches the circle at exactly one point.

Angle Relationships (Circles)

Interrelations among angles, arcs, and chords in circles.

Review Strategies

Practice with past exams, focus on weak areas, and use visual aids.