Congruency, Enlargement and Combined Transformations
Congruent
Having exactly the same shape and size.
| English | Congruent |
|---|---|
| Bahasa Melayu | Kongruen |
| 中文 | 全等 |
How it is used
After translating a triangle by the vector (5, 2), the image triangle is congruent to the object: all three sides and all three angles are unchanged, so the two triangles are identical in shape and size.
Where it shows up in SPM
Used across this Form 5 chapter to describe shapes that match exactly. Paper 2 asks you to state whether an object and image are congruent after a given transformation, and to prove triangles congruent with SSS, SAS, ASA or RHS.
Isometric transformations always produce congruent images.
Don't confuse it with
Open the chapter: Congruency, Enlargement and Combined Transformations →
Frequently asked questions
Which transformations give a congruent image?
Translation, reflection and rotation all give a congruent image, because they only move a shape without changing its size. Enlargement does not, unless the scale factor is 1 or −1, since it changes the lengths.
Do congruent shapes have to be facing the same way?
No. Congruent shapes can be turned or flipped and still be congruent, as long as their sides and angles match.
A shape and its mirror image after a reflection are congruent even though they face opposite ways.