Design and Communication Graphics

1. Design and Communication Graphics Principles of Transformation Geometry and their applications

2. Worksheet 1

3. Worksheets 1, 2 & 4 Having completed these worksheets, the students should be able to • Construct the images of plane figures under translations • Identify that the shape and size of objects remain the same under a translation • Translate figures specific distances in horizontal, vertical and inclined directions • Construct a right-angle in a semi-circle • Construct the perpendicular bisector of a line

4. Worksheet 1 Proof: The angle of a triangle in a semi-circle is 900 B Isosceles Triangle Y x R x Y C A R R M • Joining the centre M to B create two isosceles triangles As the distance from the centre of circle to the circumference is equal to the radius, the base angles must be equal. • A + B + C = 1800 • 2 X + 2 Y = 1800 Therefore X + Y = 900

5. Worksheet 2

6. Worksheet 3

7. Worksheet 3 Having completed this worksheet, students should be able to • Apply knowledge of translations in solving solids in contact problems • Apply the principles of parallel lines in solving the problems • Locate the point of contact between a cone and a sphere

8. Worksheet 4

9. Worksheet 5

10. Worksheet 5 Having completed this worksheet, the students should be able to • Appreciate the existence of translations in the design and construction of buildings and structures • Identify how different shapes can be translated to create structures • Translate a parabola along a line in a vertical position • Determine the intersection of a parabola that is translated along an inclined line with the horizontal plane

11. Worksheet 6

12. Worksheets 6, 7 & 8 Having completed this worksheet, the students should be able to • Identify and construct axes of symmetry in - geometric shapes - buildings - nature - everyday objects • Recognise that objects can have more than one axis of symmetry • Construct the images of plane figures under axial symmetry • Construct a composite of two reflections in two perpendicular lines • Use the method of axial symmetry to find the point of contact between a given ellipse and a tangent

13. Worksheet 7

14. Worksheet 8

15. Worksheet 9

16. Worksheet 9 Having completed this worksheet, the students should be able to • Construct a parabola as a plane locus given the position of the directrix and the focus • Determine the axes of reflection which map a series of points on the directrix of a parabola onto the focus

17. Worksheet 10

18. Worksheets 10, 11, 12 & 13 Having completed this worksheet, the students should be able to • Construct the rotation of a plane figure given the centre and angle of rotation • Appreciate that the rotation through 60o of an equilateral triangle about one of its vertices will produce a hexagon • Recognise that all polygons can be constructed using a rotation of a triangle • Inscribe a polygon in a circle • Measure the angle of rotation having found the image

19. Worksheet 11

20. Worksheet 12

21. Worksheet 13

22. Worksheet 14

23. Worksheet 14 Having completed this worksheet, the students should be able to • Apply knowledge of rotations to solve the rotation of geometric solids. • Rotate a geometric solid into various positions with its surfaces on various planes.

24. Worksheet 15

25. Worksheet 15 Having completed this worksheet, the students should be able to • Use the principle of loci as a problem solving tool • Construct loci in relation to circles and lines in one plane • Construct the plan of a sphere of given radius so that it is in mutual contact with two given spheres • Construct a common external tangent to two given circles of unequal radius • Construct the image of a plane figure under a rotation through a given angle

26. Worksheet 16

27. Worksheets 16 & 17 Having completed this worksheet, the students should be able to • Apply their knowledge of: • Translations • Central Symmetry • Axial Symmetry • Rotations in the solution of the given problems.

28. Worksheet 17