Geometry and Trigonometry (IB)

Point

A location in space with no dimensions.

Line

A one-dimensional figure extending infinitely in both directions.

Line Segment

A part of a line with two endpoints.

Ray

A part of a line that starts at a point and extends infinitely in one direction.

Plane

A flat, two-dimensional surface extending infinitely.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie in the same plane.

Acute Angle

Less than 90°.

Right Angle

Exactly 90°.

Obtuse Angle

Greater than 90° and less than 180°.

Straight Angle

Exactly 180°.

Reflex Angle

Greater than 180° and less than 360°.

Complementary Angles

Two angles whose sum is 90°.

Supplementary Angles

Two angles whose sum is 180°.

Vertically Opposite Angles

Angles opposite each other when two lines intersect, always equal.

Sum of Interior Angles

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

Pythagorean Theorem

In a right-angled triangle, a² + b² = c², where c is the hypotenuse.

Congruent Triangles

Triangles with equal corresponding sides and angles.

Similar Triangles

Triangles with equal corresponding angles and proportional sides.

Isosceles Triangle

A triangle with at least two equal sides.

Equilateral Triangle

A triangle with all sides and angles equal.

Scalene Triangle

A triangle with all sides of different lengths.

Quadrilateral

A polygon with four sides.

Parallelogram

A quadrilateral with opposite sides that are equal and parallel.

Rectangle

A parallelogram with all angles equal to 90°.

Rhombus

A parallelogram with all sides equal.

Square

A rectangle with all sides equal.

Trapezium

A quadrilateral with one pair of parallel sides.

Kite

A quadrilateral with two pairs of adjacent sides equal.

Circumference

The distance around a circle.

Area of a Circle

The space contained within a circle, calculated as A = πr².

Chord

A line segment with both endpoints on the circle.

Arc

A portion of the circumference of a circle.

Sector

A region enclosed by two radii and an arc.

Tangent Properties

A tangent to a circle is perpendicular to the radius at the point of contact.

Sine Rule

For any triangle, a/sin(A) = b/sin(B) = c/sin(C).

Cosine Rule

For any triangle, c² = a² + b² - 2ab*cos(C).