Class notes Geometry

1. Fundamentals of Geometry
Geometry begins with three undefined terms: Point, Line, and Plane.

Every other shape is built from these.
Segment Addition Postulate
● If B is between A and C, then AB + BC = AC.

Angle Types:
● Acute (< 90°)
● Right (= 90°)
● Obtuse (> 90° and < 180°)
● Straight (= 180°)




2. Triangles and Congruence
Triangles are the "building blocks" of geometry. Understanding how to
prove they are identical (congruent) is vital.
Proving Congruence

To prove two triangles are congruent, you can use:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
HL (Hypotenuse-Leg — for right triangles only)

The Pythagorean Theorem
In a right triangle with legs a and b and hypotenuse c: a² + b² = c²




3. Polygons and Quadrilaterals
A polygon is a closed plane figure formed by three or more segments.

Sum of Interior Angles:
● (n - 2) times 180° (where n is the number of sides).

Special Quadrilaterals:
● Parallelogram: Opposite sides are parallel and congruent.
● Rhombus: A parallelogram with four congruent sides.
● Rectangle: A parallelogram with four right angles.
● Square: A regular quadrilateral (both a rhombus and a rectangle).