Geometry  Angles, Shapes and Area  Revised
This course will guide you through different areas of Geometry such as points, lines, angles, triangles, circles, transf
Description
This course in Geometry is for high school and secondary school students. The course will guide you through several different areas of Geometry such as points, lines, angles, triangles, and circles, as well as transformations and area.
The course starts off with synthetic geometry giving you an overview of the different types of shapes you encounter in geometry, then moves on the helping you establish geometric reasoning, to help you understand the shapes. Along with teaching you how to prove three different theorems to be true.
In the next module you will learn about working out geometry with coordinates, beginning with the equation of a straight line, working out the equation for parallel and perpendicular lines. Then the module moves on to sketching a curve without a graph, along with the translation, reflection and stretching of functions on a graph. Next you will learn different ways of working out the equation of a circle, about the tangent and normal to a circle. The last part of this module discusses geometry involving one or more lines, such as the angle between two.
The third module teaches you about working out the trigonometry for find the missing sides and angles using Sine Ratio, Cosine Ration, and the Tangent Ratio. After the module on trigonometry the module on radians for measurements with circles starts with introducing radians, using them to find the area of a sector of a circle. Then the module moves on the graphing trigonometric functions and the unit circle.
Lastly you will learn about calculating the length, area, and volume of different objects, form 3cuboids to parallelograms and trapeziums. Along with how to work out the area of compound shapes and the volume of compound solid shapes.
This course would be of great interest to anyone studying secondary or high school mathematics, or any one looing to further their knowledge and skills in Mathematical geometry and geometric reasoning.
Start Course NowModules
Synthetic Geometry

Synthetic Geometry  Learning Outcomes

Properties of Shapes

Geometric Reasoning 1

Geometric Reasoning 2

Geometric Reasoning 3

Geometric Reasoning 4

Proof of Theorem 11

Proof of Theorem 12

Proof of Theorem 13

Synthetic Geometry  Lesson Summary
Coordinate Geometry

Coordinate Geometry  Learning Outcomes

Geometry with Coordinates

Equation of a Straight Line

Parallel Lines

Perpendicular Lines

The Graphs of y=kx^n

Translation of Functions

Reflection of Functions

Stretching Functions

General Transformation of Functions

Equation of a Circle 1  Centre (0,0)

Equation of a Circle 2  (Centre Not 0,0)

Equation of a Circle 3

Diameter of a Circle

Tangent and Normal to a Circle

Touching Circles

Prove that a Line is a Tangent to a Circle

Distance From a Point to a Line

Angle Between 2 Lines

Dividing a Line Segment in a Given Ratio

Coordinate Geometry  Lesson Summary
Trigonometry

Trigonometry  Learning Outcomes

Finding Angles with Sine Ratio

Finding Sides with the Sine Ratio

Finding Angles with the Cosine Ratio

Finding Sides with the Cosine Ratio

Finding Angles with the Tangent Ratio

Finding Sides with the Tangent Ratio

Finding a Missing Side with the Sine Rule

Finding a Missing Angle with the Sine Rule

Problem Solving with the Cosine Rule

Trigonometry  Lesson Summary
Radians

Radians  Learning Outcomes

Introducing Radians

Using Radians to Find Area of Sector

Sketching and Matching Trigonometric Functions

Graphing Trig Functions. y = sinx  Calculator Work – in Degrees

Graphing Trig Functions. y = 3sin2x  Valculator Work – in Radians

Introducing the Unit Circle

The Unit Circle – Drawing Sine and Cosine

Comparing Degrees to Radians on the Unit Circle

Solving Trigonometric Equations

Proving The Sine Rule

Proving the Cosine Rule

Proving Trigonometric Identity  (Sin squared + cos squared = 1)

Finding Areas with Trigonometry

3D Trigonometry  The Cuboid

3D Trigonometry  Rectangular Based Pyramid

Area of a Segment

Radians  Lesson Summary
Length, Area and Volume

Length, Area and Volume  Learning Outcomes

Circumference of a Circle

Area of a Circle

Finding Radius and Diameter of a Circle From its Perimeter

Finding Radius and Diameter From Area of Circle

Area of Trapezium

Area of Acute Angled Triangles

Area of Obtuse Angled Triangles

Area of Parallelogram

Area of Rectangles

Area Compound Shapes (Rectangles)

Area of Compound Shapes

Area of Compound Shapes (Triangles)

Volume and Surface Area

Sectors and Arcs

Area of a Segment

Volume of Compound Solid

Length, Area and Volume  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Discuss applying and using geometric reasoning to solve problems/work out solutions
 Discuss the concepts and processes used to prove a theorem to be true
 Discus working out the equation of both parallel and perpendicular lines
 Discuss the translation, reflection and stretching of functions
 Calculate the equation of a circle
 Recognize how to find angles using the sine, cosine and tangent ratios
 Recognize how to find sides on a triangle using the sine, cosine and tangent ratios
 Discuss what Radians are and their uses
 Identify how to sketch a trigonometric function on a graph
 Recognize how to solve trigonometric equations
 Recognize how to prove the sine and cosine rules to be true
 Calculate areas of geometric shapes using trigonometry
 Calculate the length, area and volume of different shapes
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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