Geometry

Angles

Types of angles

            Adjacent and vertical angles

            Angles at the intersection of two lines by a third

            Parallelism of two lines

            Angles with correspondingly parallel or perpendicular sides

            Angle bisector. Angles between bisectors

Properties of angles of a convex polygon

            Properties of angles of a triangle

            Properties of angles of a convex n-gon

Segments

Basic theorems about segments

            Thales' theorem

            Theorem on proportional segments

            Direct and converse theorems of Ceva

            Direct and converse theorems of Menelaus

Bisector, median, height, and midline of a triangle

            Bisector of a triangle

            Median of a triangle

            Height of a triangle

            An orthocentric triangle

            The middle line of a triangle

Locuses of points on a plane

Areas of figures

Formulas for finding the area of a triangle

            Heron's formula

            Formulas for calculating the area of an equilateral triangle

Formulas for finding the area of a convex quadrilateral

            Area of an arbitrary convex quadrilateral

            Area of a parallelogram

            Area of a rhombus

            Area of a trapezoid

Formulas for finding the area of a convex polygons

            Area of a convex polygon

            Area of a regular polygons

Formulas for finding the area of a circle, a sector of a circle and a segment of a circle

Circumference

Definitions: circle, chord, tangent, internal and external tangency of circles, secant

            Circle

            Chord

            Tangent

            Internal tangency of circles

            External tangency of circles

            Secant

Central angle, inscribed angle, circumference and arc lengths

            Central angle, inscribed angle

            Circumference and arc lengths

Lengths of chords, tangents, secants and angles between them

            Lengths of chords, tangents, secants

            Angles between chords, tangents, secants

Triangles inscribed in a circle and circumscribed around a circle

            Triangles inscribed in a circle

            Triangles circumscribed around a circle

Quadrilaterals inscribed in a circle and circumscribed around a circle

            Quadrilaterals inscribed in a circle

            Quadrilaterals circumscribed around a circle