Topic 7: Similarities and Enlargement – Sample Activity

Context

Ogundipe wants to have window frame fittings in his newly constructed house. While he does his evening exercises, he sees a very beautiful window. He visits a welding workshop near his house and interacts with the welders. The welders ask for the design. Ogundipe takes the welder to the house with the beautiful window frames whose design he desires for the windows he wants installed on his house.

Support Material

Task

• As a welder, write a plan on how you will design the windows to be fitted into Ogundipe’s house.

Topic Summary

In this topic, you have leant that:

• objects are similar if they are of the same shape and the ratios of their corresponding sides are the same.
• similar objects have their corresponding angles equal.
• two polygons are similar if their corresponding angles are equal and the lengths opposite equal angles are of the same ratio.
• scale factors which are positive and are greater than the whole number one are called enlargements of the object.
• scale factors with fractions less than 1 lead to images smaller in size than their objects.
• a linear scale factor of 2 doubles the length, width, height and perimeters of two-dimensional figures.
• when a two-dimensional figure is enlarged, then the images will have an area given by (LSF)2 x Area of object.
• when a three-dimensional figure is enlarged, the volume of the image figure is given by (LSF)3 x volume of object. Thus:
  • ASF = (LSF)2
  • VSF = (LSF)3
  • Where: LSF is linear scale factor

ASF is area scale factor 1.

V VSF is volume scale factor

• thus, if the linear scale factor is 4, then the volume of the image is 64 times the volume of the object.
• an enlargement with a positive scale factor greater than 1 increases the size of the object. a centre of enlargement can be outside the object, or inside the object or at a vertex of the object or an edge.

Revision Exercise

The figure below represents a triangle in which BC is parallel to DE. With the notation in the figure determine the lengths of

(a) BC. (b) CE

2. The figure below represents an isosceles triangle KLM which has been enlarged by a scale factor of 1.5 from the centre T. Given that the image of KLM has dimensions 6 cm, 6 cm and 8 cm, find the measurements of KLM.

Triangles ABC, DEF and KLM are equilateral triangles with AB AC BC= 6 cm. DE = EF and FD = 10 cm, and KL = LM 3. = MK = 12 cm.

Calculate the ratio of

(a) AB:DE.

(b) AB:KM.

(c) AB:DF:KM.

(d) Perimeter of ABC : perimeter of DEF.

(e) Perimeter of ABC : perimeter of KLM.

(f) Perimeter of ABC: perimeter of DEF: perimeter of KLM.

3. Given the points A(2, 4) B(6,4), C(6,2) and D(2,2) with centre of enlargement E(0,2) and scale factor 1, draw the image of ABCD.

4. A trapezium ABCD with vertices A(2,2), B(2,4), C(4,4) and D(6,2) undergoes an enlargement with scale factor 1.5 and centre of enlargement at the origin (0,0). Find the coordinates of the points of the image of ABCD and the area of the image of ABCD