Geometry - Angles, Shapes and Area
Course 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 3-cuboids 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.
What you'll learn in this course?
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Trigonometry
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Transition Year Top Ups and Tasters
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Geometry
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Problem Solving
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Mathematics
Course Curriculum
- 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
- Lesson Summary
- 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
- Lesson Summary
- 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
- 3-D Trigonometry - The Cuboid
- 3-D Trigonometry - Rectangular Based Pyramid
- Area of a Segment
- Lesson Summary
- 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
- Lesson Summary
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