Problem solving with advanced similarity knowledge
I can use my knowledge of similarity to solve problems.
Problem solving with advanced similarity knowledge
I can use my knowledge of similarity to solve problems.
Lesson details
Key learning points
- A scaled version of a shape/object is very useful.
- Being able to scale the perimeter/area/volume can reduce the number of calculations.
- This knowledge of similarity can be extended to include surface area.
Common misconception
"One shape has an area that is 21% larger than another shape. I can't find the area scale factor between the shapes, since I don't know the actual area of either shape."
It is possible to find scale factors, even if only a percentage that describes their areas is given. One shape will have an area of 100%, so the other shape will have an area 21% larger, at 121%. The scale factor is 1.21 because 100% × 1.21 = 121%.
Keywords
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.
Enlargement - Enlargement is a transformation that causes a change of size.
Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Volume - The amount of space occupied by a closed 3D shape.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
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Starter quiz
6 Questions
a -
∠ABC
b -
AC
c -
DC
d -
RHS
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