Congruency, Enlargement and Combined Transformations · 5.2.1
Similarity of geometric objects
This standard requires students to understand that two geometric objects are similar when all corresponding angles are equal and all corresponding sides are in the same ratio, meaning one shape is an enlarged or reduced version of the other without changing its overall shape.
The official learning standard (5.2.1)
“Explain the meaning of similarity of geometric objects.”
What it means
This standard requires students to understand that two geometric objects are similar when all corresponding angles are equal and all corresponding sides are in the same ratio, meaning one shape is an enlarged or reduced version of the other without changing its overall shape.
How it is examined
Paper 1 questions typically ask students to identify similar shapes or determine whether given figures are similar using side ratios and angles. Paper 2 questions use similarity as a foundation for enlargement and geometry problems, requiring justification through equal angles and proportional corresponding sides.
Worked example
Rectangle A has dimensions 4 cm by 6 cm, and Rectangle B has dimensions 6 cm by 9 cm. Determine whether Rectangle A and Rectangle B are similar.
- Identify corresponding sides: the 4 cm side of A corresponds to the 6 cm side of B, and the 6 cm side of A corresponds to the 9 cm side of B.
- Calculate the ratio of each pair of corresponding sides: 6 ÷ 4 = 1.5 and 9 ÷ 6 = 1.5.
- Since both ratios are equal (1.5) and all interior angles of both rectangles are 90° (equal), the two conditions for similarity are satisfied.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Are all congruent shapes also similar?
Yes, congruent shapes have equal corresponding sides and equal angles, which is a special case of similarity where the ratio of sides equals 1. Every congruent pair is similar, but not every similar pair is congruent.
Is checking angles enough to prove similarity?
For triangles, equal corresponding angles (AA) is enough because it forces the sides into proportion. For quadrilaterals and other polygons, you must check both equal angles and proportional sides.
What does "same shape, different size" really mean mathematically?
It means every pair of corresponding angles is equal and every pair of corresponding sides has the same ratio (scale factor), so one figure is an enlargement (or reduction) of the other.