When the shape is transformed its congruent shape ends up in a different position on the plane.
For example, an ‘L’ shape remains an ‘L’ shape, but it may be upside down.
You will notice that when a shape has been transformed in these ways the original shape and the resulting shape are still congruent, that is, the perimeters, side lengths, angles, areas and shapes remain the same.
The videos in the Learning Activities 1 - 4 provide thorough explanations of these different ways of transforming shapes in a plane. Practice Taska) Use the above information on the sum of interior angles to find the missing angle (x): Geometry is important because it links many areas of mathematics including algebra, measurement, and data. To calculate the sum of the angles on a 20 sided polygon: This can be applied to a polygon with any number of sides. This relationship between the number of sides and the sum of the interior angles can be expressed as follows: Sum of interior angles = (number of sides – 2) x 180° Each of the triangles has an angle sum of 180° so for any polygon you can use an equation to calculate the sum of the interior angles of any polygon: Notice that the number of triangles created by drawing all the diagonals is 2 fewer than the number of sides in the polygon i.e. Using this ‘triangles’ strategy, use similar diagrams to show how to calculate the number of angles in Hopefully you will find the following video quite fascinating, as the graphics help demonstrate how a circle can be transformed into a rectangle, demonstrating where the formula for the area of a circle, π R2, comes from.Ĭonsidering that the sum of the interior angles in a triangle is 180°, we can workout that the sum of angles in a pentagon is 540° (3 x 180°). Circle Toolįrom Illuminations Resources for Teaching MathsĬlick on the blue d for diameter, then on the video camera, and watch the circumference of the circle.Ĭlick on the red r for diameter, then on the video camera, and watch the circumference of the circle. Go to the following link from the Maths is Fun website to find out more about a circle: Circleįrom the above link, you would have discovered that when you divide the circumference by the diameter you get 3.14159…which is called pi(π).īecause the radius is half the length of the diameter, it makes sense that the circumference length is 2 x Radius x π, usually written as 2 π R.Ĭlick on the following link to see a visual simulation to help you remember that the circumference is three and a bit (3.14159…) times the length of the diameter, or six and a bit times (2 x 3.14159…) the length of the radius.
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