Concept 6.1
Same Shape, Any Size
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
Two polygons with the same number of sides are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (proportion).
The intuition
Similar means the same shape, possibly a different size: a photo and its enlargement. Angles stay exactly the same; lengths all scale by one common factor.
So the test is never 'are the sides equal?' A triangle with sides 3, 4, 5 and one with 6, 8, 10 share no side lengths, yet every ratio is 2: they are similar.
The attention
Look at the ratios of corresponding sides, not whether sides are equal.
6/3 = 8/4 = 10/5 = 2 not 3 ≠ 6, 4 ≠ 8
Look hereNot here
- Look here
- The ratios of corresponding sides. Every corresponding pair gives the same ratio, 2. One common scale factor is the signature of similar figures.
- Not here
- Whether sides are equal. Equal sides is the test for congruence: same shape and same size. Similar figures are allowed to differ in size.
- What it teaches
- Before testing, be clear which relationship you are testing for.