Question 3

Two polygons are similar if their corresponding angles are equal and their corresponding sides are in the same ratio.

Step 1 — Check side ratios

Let's find the ratio of corresponding sides. Side lengths of PQRS are all 1.5 cm. Side lengths of ABCD are all 3 cm.

$\frac{PQ}{AB} = \frac{1.5}{3}$

$= \frac{1}{2}$

$\frac{QR}{BC} = \frac{1.5}{3}$

$= \frac{1}{2}$

$\frac{RS}{CD} = \frac{1.5}{3}$

$= \frac{1}{2}$

$\frac{SP}{DA} = \frac{1.5}{3}$

$\boxed{= \frac{1}{2}}$

The ratios of corresponding sides are equal.

Step 2 — Check corresponding angles

Let's compare the corresponding angles. Quadrilateral ABCD is a square. All angles in a square are 90°. So, $\angle A = \angle B = \angle C = \angle D = 90^\circ$.

Quadrilateral PQRS is a rhombus. From the diagram, its angles are not 90°. For example, $\angle P$ and $\angle R$ are acute angles. $\angle Q$ and $\angle S$ are obtuse angles. So, the corresponding angles are not equal.

Answer

The two quadrilaterals are not similar.