Plane geometry-1

Point

has no dimension, it has position only. It is represented by a dot and named with a capital letter

Line

has length only, one-dimensional. It is infinitely long and thin. Named by a lowercase letter or two points

Straight Line

is uniquely determined by two different points.

Segment

is a part of a line with a finite length. Denoted by its endpoints

Ray

is a half-line that starts at one endpoint and extends infinitely in one direction.

Surface

has length and width but no thickness, making it two-dimensional.

Plane

is a flat surface extending infinitely with no thickness. Named using a Greek letter or three non-collinear points.

Collinear Points

Three or more points lying on the same straight line.

Non-Collinear Points

Three or more points not lying on the same straight line.

Parallel Lines

Lines that are always the same distance apart and never meet.

Intersecting Lines

Lines that share exactly one common point.

Coincident Lines

Lines that share all points, meaning they are the same line.

Skew Lines

Lines that do not lie in the same plane and never intersect.

Angles

its formed by two rays sharing the same endpoint, called the vertex.

Acute Angle

An angle measuring less than 90°.

Right Angle

An angle measuring exactly 90°.

Obtuse Angle

An angle measuring greater than 90° but less than 180°.

Straight Angle

An angle measuring exactly 180°.

Reflex Angle

An angle measuring greater than 180° but less than 360°.

Congruent Angles

Angles that have the same measure.

Complementary Angles

Two angles whose sum is 90°.

Supplementary Angles

Two angles whose sum is 180°.

Vertical Angles

Angles formed by intersecting lines that are opposite and congruent.

Adjacent Angles

Two angles that share a common vertex and side but do not overlap.

Corresponding Angles

Angles in the same relative position when a transversal crosses parallel lines.

Alternate Angles

Angles on opposite sides of a transversal that cross parallel lines, having equal measures.

Measuring Angles

Angles are measured in degrees using a protractor.

Polygon

A closed plane figure with at least three line segments.

Convex Polygon

A polygon where all interior angles are less than 180°.

Concave Polygon

A polygon with at least one interior angle greater than 180°.

Regular Polygon

A polygon that is both equilateral and equiangular.

Quadrilateral

A polygon with four sides and four vertices.

Square

A quadrilateral with four equal sides and four right angles.

Rectangle

A quadrilateral with opposite sides equal and four right angles.

Parallelogram

A quadrilateral with opposite sides parallel and equal in length.

Rhombus

A quadrilateral with four equal sides and opposite angles equal.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Kite

A quadrilateral with two pairs of adjacent sides equal in length.

Circle

The set of all points in a plane that are equidistant from a fixed center.

Radius

A line segment from the center of the circle to any point on the circle.

Diameter

A line segment passing through the center of the circle, equal to twice the radius.

Circumference

The perimeter of a circle, calculated as 2πr or πd.

Chord

A line segment joining two points on a circle.

Secant

A line that intersects a circle at two points.

Tangent

A line that touches a circle at exactly one point.

Arc

A section of a circle between two points.

Central Angle

An angle whose vertex is at the center of the circle.

Inscribed Angle

An angle formed by two chords in a circle sharing an endpoint.

Thales' Theorem

An angle inscribed in a semicircle is always a right angle.

Triangle

A three-sided polygon.

Isosceles Triangle

A triangle with two equal sides.

Equilateral Triangle

A triangle with all three sides equal.

Scalene Triangle

A triangle with all three sides of different lengths.

Right Triangle

A triangle with one right angle.

Obtuse Triangle

A triangle with one obtuse angle.

Acute Triangle

A triangle with all acute angles.

Triangle Interior Angles

The sum of the interior angles in a triangle is always 180°.

Pythagorean Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

Median

A line from a triangle's vertex to the midpoint of the opposite side.

Altitude

A perpendicular segment from a vertex to the opposite side.

Midsegment

A line joining the midpoints of two sides of a triangle, parallel to the third side.

Circumcircle

A circle passing through all three vertices of a triangle.

Incircle

The largest circle that fits inside a triangle, touching all three sides.

Similarity

if their corresponding angles are equal and their sides are proportional.

Congruence

if they have the same shape and size.

Euclid's Theorem

Relates the altitude of a right triangle to the geometric mean of two segments of the hypotenuse.