Geometry eLesson
Geometry Lesson 1
Lines and angles
Angles
Worked example
Perpendicular and parallel lines
Worked example
Polygons
What is a polygon
Types of polygons
Polygons classified according to number of sides
Eight worked examples
Hexagon
Triangles
Types of triangles
Worked example
Area of a triangle
Pythagorean Theorem
Similar triangle
Congruent triangles
Exterior angles
Worked example
Ratios in a right triangle
Median of a triangle
Some important theorems
Midpoint theorem
Basic proportionality theorem
Interior angle bisector theorem
Exterior angle bisector theorem
Quadrilaterals
Parallelogram
Rhombus
Rectangle
Square
Worked example
Trapeziod
Circles
Four worked examples
Mensuration
Cuboid (rectangular box)
Cube
Worked example
Cylinder
Right circular cone
Sphere
Pyramid
10 worked examples with detailed explanations
22 worked examples with detailed explanations
Coordinate Geometry Lesson 1
The Cartesian coordinate system
Parallel and perpendicular lines
Slope of a straight line
Parallel lines
Perpendicular lines
Worked example
Midpoint theorem
Exercise
Distance formula
Corollary
Example
Section formula
Worked example
Angle a line makes with a positive direction of the x-axis
Worked examples
Equation of a straight line in different forms
Slope-Intercept form
Point-slope form
Two-point form
Intercept form
Normal (or perpendicular) form
General form
Condition for being parallel
Condition for being perpendicular
Four worked examples
Families of lines
One parameter family of lines
Examples of one parameter families of lines
Two worked examples
Position of two points relative to a line
Worked example
Distance of a point from a line
Two worked examples
Translation of axes
Worked example
Parametric equations
Worked example
Other curves (conic sections)
Rectangular hyperbola
Parabola
Two worked examples
Hyperbola
Ellispse
Two worked examples
Coordinate Geometry Lesson 2
37 worked examples (including data sufficiency) with detailed explanations
Circles
Prerequisites for this lesson
What is a circle
Tangent to a circle
What is a tangent
Chord of a circle
What is a chord
What is a secant
The crossed chord theorem
Angle properties of a circle
The radian measure
Angle at the center of a circle
Sector of a circle
Worked example
Segment of a circle
Worked examples
Angles in the same segment of a circle
Worked example
Angle in a semi-circle
Worked example
Arc properties of circles
Major and minor arcs
Axiom of equal arcs
Arc length
Worked example
Tangent properties of circles
Tangents drawn from an external point of a circle
Worked example
Alternate segment theorem
Worked example
Common tangents to circles
Length of common tangent
Important formulas
Important properties of circles
Worked example
Polygons in circles
Annulus
Worked example
Five worked examples
Other lessons in the “Geometry Course Module”
Angles in a polygon
Area of triangles
Parallelograms
Cyclic quadrilaterals
Pythagorean triplets
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