Geometry, Constructions and Enlargements

Geometry is the study of shapes. Key terms such as theorem, proof, axiom, corollary, converse, implies must be understood. I recommend learning examples for each key term.

CONSTRUCTIONS.

For this section, bring a compass, a ruler, a protractor and set-squares. Students may be asked to perform one of the following constructions in Paper 2:

16. Circumcentre and circumcircle of a given triangle, using only straight-edge and compass.

17. Incentre and incircle of a given triangle, using only straight-edge and compass.

18. Angle of 60°, without using a protractor or set-square.

19. Tangent to a given circle at a given point on it.

20. Parallelogram, given the length of the sides and the measure of the angles.

21. Centroid of a triangle.

The numbers above have been taken from the syllabus. See your textbook for further explanation. Students will not be asked to prove any of the theorems. Instead, students will be required to use the results of the theorems as explanation for their answers.

ENLARGEMENTS.

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Drawing enlargements: To construct the image of a given figure under an enlargement, we need: i The centre of enlargement ii The scale factor of the enlargement.

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Scale factor: The scale factor is the difference in size between two images (i.e. the ratio between the two images). When a shape is enlarged all the lengths are multiplied by the scale factor and all angles remain the same. l

Formula: The scale factor, k, is given below:

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Area and enlargements: When a figure is enlarged by a scale factor k, the area of the image figure is increased by a scale factor k2.

Area of Image = k2(Area Object)