What is true of two similar shapes?

Their matching angles are equal. Their sides are also in the same ratio.

Lengths are enlarged by a scale factor of 3. What happens to the area?

× 9. Area is multiplied by the scale factor squared.

Lengths are enlarged by a scale factor of 2. What happens to the volume?

× 8. Volume is multiplied by the scale factor cubed.

What does congruent mean?

the same shape and the same size. One would fit exactly on top of the other.

Similar and congruent shapes · Cambridge IGCSE Mathematics

In plain words

Enlarge a photo and everything in it stays the same shape, just bigger. The two pictures are similar. If two shapes are exactly the same size as well, they are congruent. Similar shapes are useful because one multiplier turns every length of one into the matching length of the other.

Three things to know

Similar shapes have the same angles, and their sides are in the same ratio. That ratio is the scale factor.
If lengths are multiplied by k, areas are multiplied by k² and volumes by k³.
Congruent shapes are identical in shape and size. Triangles are congruent if they match by SSS, SAS, ASA or RHS.

Worked example

Two triangles are similar. A side of 4 cm on the small one matches a side of 6 cm on the large one. Another side of the small one is 10 cm. Find the matching side on the large one.

Scale factor = 6 ÷ 4 = 1.5.
Multiply the matching side: 10 × 1.5.
= 15 cm.

Tips and tricks

Find the scale factor from a pair of sides you know both of: big ÷ small.
Lengths × 2 means areas × 4 and volumes × 8. Don't just double everything.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Similar and congruent shapes: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is true of two similar shapes?
- They are the same size.
- Their matching angles are equal. (the answer)
- Their areas are equal.
- They have different angles.
Their sides are also in the same ratio.
Lengths are enlarged by a scale factor of 3. What happens to the area?
- × 3
- × 6
- × 9 (the answer)
- × 27
Area is multiplied by the scale factor squared.
Lengths are enlarged by a scale factor of 2. What happens to the volume?
- × 2
- × 4
- × 6
- × 8 (the answer)
Volume is multiplied by the scale factor cubed.
What does congruent mean?
- the same shape but a different size
- the same shape and the same size (the answer)
- the same area only
- having parallel sides
One would fit exactly on top of the other.
Two similar triangles have matching sides of 5 cm and 15 cm. What is the scale factor?
- 2
- 3 (the answer)
- 10
- 75
15 ÷ 5.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 6 marks. Write your answers on paper, then check them.

Similar and congruent shapes

Cambridge IGCSE Mathematics 0580 · 6 marks · papermunch.org

Name ______________________________ Date ______________

Two similar rectangles have widths of 3 cm and 12 cm. The smaller has length 5 cm. Find the length of the larger.[2]
Show answerHide answer
20 cm. Scale factor 4.
I got this one
Two similar shapes have lengths in the ratio 1 : 3. The smaller has area 5 cm². Find the area of the larger.[2]
Show answerHide answer
45 cm². 5 × 3².
I got this one
A model is made to a scale of 1 : 10. The model has a volume of 2 cm³. Find the volume of the real object.[2]
Show answerHide answer
2000 cm³. 2 × 10³.
I got this one

Answers: Similar and congruent shapes

1. 20 cm. Scale factor 4.
2. 45 cm². 5 × 3².
3. 2000 cm³. 2 × 10³.