Geometry Basics: Points, Lines, and Segments

A point is a location in space, represented by a set of coordinates (x, y, z).
A line is a set of points that extend infinitely in two directions.
Line segments are parts of lines with a fixed length.
Rays are lines that extend infinitely in one direction from a single point.
Midpoint of a line segment: the point that divides the segment into two equal parts.
Distance formula: the formula to calculate the distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)^2 + (y2 - y1)^2).

An angle is formed by two rays sharing a common endpoint (vertex).
Types of angles:
- Acute: less than 90°
- Right: exactly 90°
- Obtuse: greater than 90°
- Straight: exactly 180°
A triangle is a polygon with three sides and three angles.
Properties of triangles:
- Sum of interior angles: always 180°
- Exterior angles: the sum of an exterior angle and its corresponding interior angle is always 180°
- Congruent triangles: triangles with the same shape and size
- Similar triangles: triangles with the same shape but not necessarily the same size
Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs of a right triangle and c is the hypotenuse.

A quadrilateral is a polygon with four sides and four angles.
Types of quadrilaterals:
- Rectangle: all angles are right angles
- Square: a rectangle with all sides equal
- Trapezoid: a quadrilateral with two pairs of opposite sides
- Rhombus: a quadrilateral with all sides equal
A polygon is a closed figure with three or more sides.
Properties of polygons:
- Sum of interior angles: (n - 2) × 180°, where n is the number of sides
- Regular polygons: polygons with all sides and angles equal
- Irregular polygons: polygons that are not regular

A circle is a set of points equidistant from a central point (center).
Properties of circles:
- Circumference: the distance around the circle
- Radius: the distance from the center to any point on the circle
- Diameter: the longest distance across the circle, passing through the center
Conic sections are curves obtained by intersecting a cone with a plane.
Types of conic sections:
- Circle: a conic section with a plane perpendicular to the cone's axis
- Ellipse: a conic section with a plane not perpendicular to the cone's axis
- Parabola: a conic section with a plane parallel to the cone's side
- Hyperbola: a conic section with a plane not parallel to the cone's side

A point is represented by a set of coordinates (x, y, z) in space.
A line is a set of points extending infinitely in two directions.
A line segment is a part of a line with a fixed length.
A ray is a line extending infinitely in one direction from a single point.
The midpoint of a line segment divides it into two equal parts.
The distance formula calculates the distance between two points (x1, y1) and (x2, y2) as √((x2 - x1)^2 + (y2 - y1)^2).

An angle is formed by two rays sharing a common endpoint (vertex).
Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are greater than 90°, and straight angles are exactly 180°.
A triangle is a polygon with three sides and three angles.
The sum of interior angles in a triangle is always 180°.
Exterior angles add up to 180° when combined with their corresponding interior angles.
Congruent triangles have the same shape and size, while similar triangles have the same shape but not necessarily the same size.
The Pythagorean theorem states that a^2 + b^2 = c^2, where a and b are the legs of a right triangle and c is the hypotenuse.

A quadrilateral is a polygon with four sides and four angles.
Rectangles have all right angles, squares are rectangles with all sides equal, trapezoids have two pairs of opposite sides, and rhombuses have all sides equal.
A polygon is a closed figure with three or more sides.
The sum of interior angles in a polygon is (n - 2) × 180°, where n is the number of sides.
Regular polygons have all sides and angles equal, while irregular polygons do not.

A circle is a set of points equidistant from a central point (center).
The circumference is the distance around a circle, the radius is the distance from the center to any point on the circle, and the diameter is the longest distance across the circle.
Conic sections are curves obtained by intersecting a cone with a plane.
Circles are conic sections with a plane perpendicular to the cone's axis, ellipses are conic sections with a plane not perpendicular to the cone's axis, parabolas are conic sections with a plane parallel to the cone's side, and hyperbolas are conic sections with a plane not parallel to the cone's side.