Starter quiz
- ______ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
- 'Pythagoras'' ✓
- The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.
- 8 cm, 15 cm, 17 cm ✓
- 8 cm, 10 cm, 12 cm
- 15 cm, 20 cm, 25 cm
- 9 cm, 15 cm, 18 cm
- 9 cm, 12 cm, 15 cm ✓
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- A right-angled triangle has a hypotenuse of 25 m. Select the possible lengths of the two shorter sides.
- 12 m and 18 m
- 15 m and 20 m ✓
- 7 m and 24 m ✓
- 8 m and 20 m
- 10 m and 15 m
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- Which of these pairs of triangles are congruent?
Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side is ______ cm.- '8' ✓
Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.- a⇔∠ABC ✓
- b⇔AC ✓
- c⇔DC ✓
- d⇔RHS ✓
Exit quiz
- Two shapes are ______ if the only difference between them is their size. Their side lengths are in the same proportions.
- 'similar' ✓
- The multiplier between the surface areas of a pair of similar objects is . Select the correct statements.
- The multiplier between their corresponding edge lengths is ✓
- The multiplier between their corresponding edge lengths is
- The multiplier between their volumes is
- The multiplier between their volumes is ✓
- The multiplier between their volumes is
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- Shapes X and Y are similar to each other. The volume of shape Y is 216 times larger than the volume of shape X. The linear scale factor from X to Y is ______.
- '6' ✓
- Shapes X and Y are similar. The perimeter of shape Y is 125% of the perimeter of shape X. Work out the area scale factor from X to Y.
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- ✓
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Pyramid A and pyramid B are similar. The surface area of pyramid A is 50 cm² and its volume is 120 cm³. The surface area of pyramid B is 450 cm². Calculate the volume of pyramid B.- 3480 cm³
- 3240 cm³ ✓
- 1920 cm³
- 1080 cm³
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Cuboid A and cuboid B are similar. The volume of cuboid B is 7680 cm³. The surface area of B is ______ cm².- '2528' ✓
Worksheet
Presentation
Video
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.