- Year 10
Problem solving with similarity
I can use my knowledge of similarity to solve problems.
Lesson details
Key learning points
- A scaled version of a shape is very useful.
- Being able to scale the perimeter can reduce the number of calculations.
- Enlargement (transformations) and similar shapes are connected.
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.
Common misconception
A ratio of 1 : 400 for a scale model of a car to a real car will have units of cm and metres, because a scale model is measured in cm and a real car is measured in metres.
Unless the scale explicitly includes different units of measure for each part, you must always use the same unit for each part of a ratio. So, 1 : 400 should be seen as 1 cm : 400 cm, not 400 metres, which is far too long for a car!
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of these pairs of triangles are congruent?
Q2.Pythagoras’ theorem states that the of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Q3.The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.
Q4.A right-angled triangle has a hypotenuse of 65 mm. Select the possible lengths of the two shorter sides.
Q5.Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side $$x$$ is cm.
Q6.Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.
a - ∠ABC
b - hypotenuse
c - adjacent
d - RHS
Assessment exit quiz
6 Questions
Q1.Similarity can be used in architecture or in mechanical drawings to make a drawing of a real world object.
Q2.This is a scale drawing of a van. The height of the van is metres.
Q3.This is a scale drawing of a van. The length of the van is metres.
Q4.Sam has attempted to enlarge this object by a scale factor of 2.5. Which statements are correct?
Q5.The dashed triangle shows the route a bird took between its nest N, a lake L and an old manor house M. The bird flies direct from its nest to the manor and then to the lake. How far does it fly?
Q6.The dashed triangle shows the route a bird took between its nest N, a lake L and an old manor house M. The bird flies direct from its nest, N, to the lake, L. The distance the bird flies is km.
