Class 10 Maths · Chapter 6 · Topic 1 of 5
Similar means the same shape
Similar means the same shape, even when the size changes.
Ideas you’ll use
- Similar figures
- Figures with the same shape, though their sizes may differ. Similar polygons have equal corresponding angles and proportional corresponding sides.
Understand it, one idea at a time
Choose an idea. Follow its reason, calculation and clue in the picture.
Enlarge every side together
- Correspondence
- Each side in the violet triangle has the same scale factor.
- Same angle
- Equal corresponding ratios preserve the shape.
Compare matching sides
A scale factor must multiply every corresponding side equally.
3,4,5 → 6,8,10: every side ×2In the picture: Compare matching sides of the two triangles.
Read all the reasoning together
Compare matching sides
A scale factor must multiply every corresponding side equally.
3,4,5 → 6,8,10: every side ×2Separate similarity from congruence
Congruent shapes have equal size too. They are similar with scale factor 1.
Congruent ⇒ similar; similar need not ⇒ congruentDo not overgeneralise angle matching
Equal angles alone do not guarantee similar general polygons.
A square and a non-square rectangle both have right angles
Similar means the same shape, even when the size changes.
Worked example: Compare corresponding lengths
Sides 3, 4, 5 and 6, 8, 10 have ratio 1:2Every side has the same multiplier. A square and a non-square rectangle both have right angles, but do not have the same shape. For general polygons, equal angles alone are not enough.
Read the supporting explanation
If every length doubles, the shape stays the same. Congruent figures have the same shape and the same size, so they are similar with scale factor 1. Similar figures need not be congruent.
Go deeper: Shape cannot be proved by appearance
A drawing can suggest a match, but use stated angles, side ratios or a valid triangle criterion to prove it. Do not measure the screen to create a missing fact.
Your turn
Try the idea yourself. Show your reasoning, then compare.
Question
Are all circles similar? Are all rectangles similar?
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