3. By drawing and marking in the lines of symmetry, fi nd the number of lines of symmetry in each of the parallelograms to the right.
(i) 6cm 4cm (ii) 6cm 14cm 6cm 12cm (iii)
4. Find the value of x and y in the following diagrams of parallelograms. All units are in metres.
(i) 35 60 5y+10 9cm (ii) 5x + 4 3y – 6 34 42
6. Shown below is a diagram used as part of the proof for the theorem which states: The diagonals of a parallelogram bisect one another.
Look at triangle 1 ∆ ADE and triangle 2 ∆ BCE .
State why these triangles are congruent using angles and sides in your answer.
A 1 E 2 B C D 4x+8 6cm 4cm 10cm 6cm 12cm 12cm 7cm 14cm (iv) 18m 8m 20m
5. Find the area of the shaded parallelograms in the diagrams below.
(i) 4cm 12cm (ii) 8m 18m
23.5 Transformations of objects
A transformation is a process which changes the position or the size and direction of a shape.
By the end of this section you should:
● understand the terms translation, central symmetry, axial symmetry and rotation
● be able to draw the image of objects under translation, central symmetry, axial symmetry and rotation
The object is the name given to the shape you start with. The image is the name given to the shape after the transformation.
The point A’ is the image of point A under some transformation. The point B’ is the image of point B under some transformation. The point C’ is the image of point C under some transformation.
B A Object C B' A' 382 Linking Thinking 1 Image C'