Congruency, Enlargement and Combined Transformations · Form 5
Congruent vs similar shapes: what's the difference?
Congruent shapes have exactly the same shape AND size, so all corresponding sides and angles are equal. Similar shapes have the same shape and equal corresponding angles, but their sizes may differ, with corresponding sides in one common ratio.
Same size, or just the same shape?
Congruent means identical: every pair of corresponding sides is equal and every pair of corresponding angles is equal, so one shape fits exactly onto the other. Similar means the shapes share equal corresponding angles and their corresponding sides keep one common ratio, but the actual lengths may differ.
A 3 cm square and a 6 cm square are similar (ratio 1 : 2) but not congruent, while two 5 cm squares are both similar and congruent.
Why every congruent pair is also similar
Congruent shapes are just a special case of similar shapes where the common ratio (the scale factor) equals 1. So 'congruent' is really 'similar, at the same size.'
An enlargement always produces a similar image; when the scale factor is 1 (or −1) that image is also congruent to the object, because no lengths have actually changed.
How to tell them apart, and the usual slip
To decide, look at the corresponding sides: if they are equal, the shapes are congruent; if they are only proportional (same ratio, different lengths), they are similar. The usual mistake is treating 'similar' as 'looks alike' in mathematics it is precise: equal corresponding angles AND corresponding sides in one common ratio.
Another slip is thinking congruent shapes must face the same way, when a reflected or rotated copy is still congruent.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I tell if two shapes are congruent or just similar?
Congruent shapes are identical in shape and size, so matching sides and matching angles are exactly equal. Similar shapes have equal corresponding angles and sides in the same fixed ratio, but different overall size.
Check the ratio of side lengths: a ratio of 1 means congruent; any other constant ratio means similar only.
In an exam, how do I show that two shapes are congruent?
State the congruence test used, such as SSS, SAS, ASA, or RHS, and match up corresponding vertices, sides, and angles in the correct order, for example triangle ABC ≡ triangle PQR. Naming vertices in the wrong correspondence order is a common mistake that loses marks even when the shapes are genuinely congruent.
What's the pitfall when two shapes look alike but sizes aren't checked?
Two shapes can look alike but only be similar, not congruent, if their sizes differ. Always compare actual side lengths or use a stated congruence or similarity condition rather than judging by eye - SPM questions often include a similar, not congruent, pair to test this.