Starter quiz
- Which of these pairs of triangles are congruent?
- 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.
- 'sum' ✓
- The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.
- 5 cm, 10 cm, 15 cm
- 5 cm, 12 cm, 13 cm ✓
- 12 cm, 28 cm, 24 cm
- 20 cm, 24 cm, 26 cm
- 10 cm, 24 cm, 26 cm ✓
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- A right-angled triangle has a hypotenuse of 65 mm. Select the possible lengths of the two shorter sides.
- 39 mm and 52 mm ✓
- 20 mm and 35 mm
- 20 mm and 25 mm
- 16 mm and 63 mm ✓
- 32 cm and 40 cm
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Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side is ______ cm.- '24' ✓
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 ✓
Exit quiz
- Similarity can be used in architecture or in mechanical drawings to make a ______ drawing of a real world object.
- 'scale' ✓
This is a scale drawing of a van. The height of the van is ______ metres.- '2.4' ✓
- This is a scale drawing of a van. The length of the van is ______ metres.
- '4.8' ✓
Sam has attempted to enlarge this object by a scale factor of 2.5. Which statements are correct?- Sam is wrong, you can't have a decimal scale factor
- The object and image aren’t similar because Sam enlarged it incorrectly. ✓
- The object and image aren't similar as the angles are not invariant ✓
- Object and image are similar as all enlargements are similar to their object.
- The object and image are similar as the angles are invariant
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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?- 14 km
- 8 km
- 6 km
- 1.4 km ✓
- 0.2 km
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- 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.
- '1' ✓
Worksheet
Presentation
Video
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.
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!
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.