Congruency, Enlargement and Combined Transformations · 5.1.1
Congruent and non-congruent shapes
This standard asks students to compare two or more geometric shapes and decide whether they are congruent, meaning they have exactly the same side lengths and angles and would fit perfectly on top of each other, or non-congruent, where at least one corresponding side or angle differs, even if the shapes look similar.
The official learning standard (5.1.1)
“Differentiate between congruent and non-congruent shapes based on sides and angles. Suggested Activity: The use of dynamic geometry software is encouraged throughout this topic.”
What it means
This standard asks students to compare two or more geometric shapes and decide whether they are congruent, meaning they have exactly the same side lengths and angles and would fit perfectly on top of each other, or non-congruent, where at least one corresponding side or angle differs, even if the shapes look similar.
How it is examined
This standard is tested in Paper 1 as objective items showing pairs of shapes with marked sides or angles, asking students to identify whether they are congruent, and may form the introductory reasoning step of a Paper 2 geometry question before proving triangle congruency using specific conditions like SSS or SAS.
Worked example
Triangle ABC has sides AB = 5 cm, BC = 7 cm, AC = 6 cm. Triangle PQR has sides PQ = 5 cm, QR = 7 cm, PR = 6.2 cm.
State, with a reason, whether triangle ABC and triangle PQR are congruent.
- Compare the first pair of corresponding sides: AB = PQ = 5 cm ✓, BC = QR = 7 cm ✓
- Compare the third pair of corresponding sides: AC = 6 cm, PR = 6.2 cm, these are not equal.
- Since not all three pairs of corresponding sides are equal, the SSS condition for congruency is not satisfied.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Do congruent shapes have to be facing the same direction?
No, congruent shapes can be rotated, reflected or translated from one another and still be congruent, as long as all corresponding sides and angles are equal; orientation on the page does not affect congruency, only the actual measurements matter.
Is it enough to check that shapes look the same size to say they are congruent?
No, visual similarity is not proof; you must confirm that every pair of corresponding sides and every pair of corresponding angles are exactly equal using given measurements or a recognised congruency condition, since two shapes can look alike but differ slightly in one measurement.
What's the difference between congruent and similar shapes?
Congruent shapes are identical in both size and shape, every corresponding side and angle is equal; similar shapes have the same shape (equal corresponding angles) but can differ in size, with corresponding sides in a constant ratio rather than being equal, which is covered in the next standard on similarity.