📏 Scaling Secrets: Mastering Similarity in Shapes!

Have you ever built a tiny model car or drawn a small map of your neighbourhood? Those mini-versions look the same, just **smaller or larger**. That is the idea of *similarity*. In O-Level exams, being able to switch between sizes confidently can earn easy marks, so let’s dive in!

Understanding Similarity & Scale Factor

Two shapes are **similar** when their corresponding angles are equal and their sides are in the same ratio.
This constant ratio is called the *scale factor* $k=\dfrac{\text{new length}}{\text{original length}}$ .
To enlarge, multiply every original side by $k$ ; to reduce, divide by $k$ .

Worked Example: Mystery Side of a Triangle

Problem: Triangle PQR is similar to triangle XYZ. Side PQ corresponds to XY. Given PQ = 5 cm and XY = 8 cm, and PR = 6 cm, find the length of XZ. Solution: Step 1: Find the scale factor.

k = \frac{XY}{PQ} = \frac{8}{5} = 1.6

Step 2: Apply the scale factor to the matching side.

XZ = k \times PR = 1.6 \times 6 = 9.6\text{ cm}

. Answer:

XZ = 9.6\text{ cm}

. Keep practising similar questions and soon you’ll spot these relationships **instantly**!