Same shape, any size
Two figures are similar if one can be zoomed to fit exactly on the other.
A photo in two sizes
The same photograph of the Taj Mahal is printed in two sizes: a small stamp-size print and a big postcard-size print.
The two prints are not the same size. Are they the same shape?
Is the big print the same shape as the small print?
What this lesson covers
The idea
Figures having the same shape but not necessarily the same size are similar; so all circles are similar, all squares are similar and all equilateral triangles are similar.
A photo in two sizes
The same photograph of the Taj Mahal is printed in two sizes: a small stamp-size print and a big postcard-size print.
The two prints are not the same size. Are they the same shape?
Is the big print the same shape as the small print?
- Yes. Same shape, only the size is different.
- No. A different size means a different shape.
- Only if the two prints are the same size.
Zoom to fit
Each picture shows two figures. Turn the zoom dial to make the blue figure bigger or smaller. Can it fit exactly on the orange dashed one? Then say whether they have the same shape.
Same shape, not always the same size
Figures with the same shape but not necessarily the same size are called similar figures. All circles are similar, all squares are similar and all equilateral triangles are similar.
Think of the zoom dial: if one figure can be made bigger or smaller until it fits exactly on the other, they are similar. A circle and a square never fit, so they are not similar.
Notes
Similar figures have the same shape but not necessarily the same size. All circles are similar, all squares are similar and all equilateral triangles are similar.
Check yourself
Which pair is always similar, whatever the sizes?
A photograph is stretched so that it becomes wider but not taller. Is the new picture similar to the old one?
Two photographs of a person are printed in exactly the same size. One shows the person at age 10 and the other at age 40. Are the photographs similar?
Which pair is not similar?
- Two rectangles. No. One rectangle can be long and thin, another nearly square. They have different shapes.
- Two circles — correct. Yes! Zoom one circle and it fits the other, whatever the radii.
- Two triangles. No. A tall thin triangle and a flat wide one have different shapes. Equilateral triangles are all similar, but triangles in general are not.
- Yes. It is still the same photograph.. Stretching in one direction changes the shape. A zoom must change the picture by the same amount in every direction.
- Yes, if it is stretched only a little.. Even a small stretch in one direction changes the shape.
- No. The shape has changed. — correct. Yes! Stretching one way is not a zoom, so the shape is no longer the same.
- No. They are the same size but not the same shape. — correct. Yes! Similar means the same shape. The same size does not make the shape the same.
- Yes. They are the same size.. Same size does not mean same shape. The face at 40 is not a zoomed copy of the face at 10.
- Yes. Both show the same person.. Showing the same person does not make the shape of the picture the same.
- Two squares, with sides 3 cm and 7 cm. All squares are similar: zoom one and it fits the other.
- Two equilateral triangles, with sides 4 cm and 9 cm. All equilateral triangles are similar.
- A circle and a square — correct. Yes! A circle has no corners and a square has four. No zoom makes one fit the other.