Question

State whether the following quadrilaterals are similar or not:

Answer 1

Similar polygons:

Two figures are said to be similar if and only if their corresponding angles are equal and their corresponding sides are in the same ratio.

Now, in Quadrilateral, $PQRS$ and Quadrilateral, $ABCD$

Clearly, corresponding angles not equal.

[Since, all the angle are in Quadrilateral, $ABCD$ are ${90}^{\circ }$ but all the angle are in Quadrilateral $PQRS$ not equal to ${90}^{\circ }$.

So, given quadrilaterals are not similar.

Here, ratios of corresponding sides are equal.

ex: $\frac{AB}{BC}=\frac{3cm}{3cm}=1cm$

$\frac{PQ}{QR}=\frac{1.5cm}{1.5cm}=1cm$

$\Rightarrow \frac{AB}{BC}=\frac{PQ}{QR}$

Similarly, the ratio of other corresponding sides are also equal.

But corresponding angles not equal.

Hence, Given quadrilaterals are not similar.