State whether the following pair of polygons are similar or not.

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True

False

answer is B.

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Detailed Solution

Given figures are,
Question Image

Consider the quadrilaterals ABCD and PQRS.
Write the corresponding sides in the ratio,

\frac{AD}{PS} = \frac{2}{2}

\Rightarrow \frac{AD}{PS} = 1

\frac{AB}{PQ} = \frac{4}{4}

\Rightarrow \frac{AB}{PQ} =

\frac{CD}{RS} = \frac{4}{4}

\Rightarrow \frac{CD}{RS} = 1

And the all angles of the quadrilaterals ABCD are same.
Such that ,

∠ A = ∠ B = ∠ C = ∠ D = 90 °

and for quadrilateral PQRS

∠ P = ∠ R ≠ 90 °

and

∠ Q = ∠ S ≠ 90 °

.
As the ratio of the corresponding sides of a quadrilateral, ABCD and PQRS are same but their corresponding angles are not equal.
So, the quadrilateral ABCD and PQRS are not similar.
Therefore, the statement is false.
The corrected statement will be that the given pairs of quadrilaterals are not similar.
Option 2 is correct.

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