Geom

Point

An exact location with no size.

Line

Extends infinitely in both directions, determined by two points.

Line segment

Part of a line between two endpoints.

Ray

Starts at a point and extends infinitely in one direction.

Plane

A flat two-dimensional surface extending infinitely.

Angle

Formed by two rays with a common endpoint (vertex).

Polygon

A closed figure made of straight line segments (triangles, quadrilaterals, etc.).

Circle

Set of points at a fixed distance (radius) from a center.

Acute angle

An angle measuring less than 90°.

Right angle

An angle measuring exactly 90°.

Obtuse angle

An angle measuring between 90° and 180°.

Straight angle

An angle measuring exactly 180°.

Reflex angle

An angle measuring more than 180°.

Pythagorean theorem

In a right triangle, if legs are a and b and hypotenuse is c, then a² + b² = c².

Triangle area formula

A = 1/2 * base * height.

Circumference of a circle

C = 2πr, where r is the radius.

Circle area formula

A = πr², where r is the radius.

Midpoint formula

Midpoint between points (x1,y1) and (x2,y2) is ((x1+x2)/2, (y1+y2)/2).

Distance formula

Distance between points (x1,y1) and (x2,y2) is d = √((x2-x1)² + (y2-y1)²).

Regular polygon area formula

Area of a regular polygon is A = 1/2 * apothem * side * n.

Similarity in geometry

Two figures are similar if they have the same shape but may have different sizes.

Congruence in geometry

Two figures are congruent if they have the same shape and size.

Transformations

Operations that alter the form of a figure, including translation, rotation, reflection, and dilation.