Design and Communication Graphics Principles of Transformation Geometry and their applications

Worksheet 1

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

Y x x Y A B C M Proof: The angle of a triangle in a semi-circle is 90 0 Joining the centre M to B create two isosceles triangles R R R 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 = X + 2 Y = Therefore X + Y = 90 0 Isosceles Triangle Worksheet 1

Worksheet 2

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

Worksheet 4

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

Worksheet 6

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

Worksheet 7

Worksheet 8

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

Worksheet 10

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 60 o 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

Worksheet 11

Worksheet 12

Worksheet 13

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.

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

Worksheet 16

Worksheets 16 & 17 Having completed this worksheet, the students should be able to Apply their knowledge of: 1.Translations 2.Central Symmetry 3.Axial Symmetry 4.Rotations in the solution of the given problems.

Worksheet 17