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State whether the following quadrilaterals are similar or not :

State whether the following quadrilaterals are similar or not. NCERT Class 10 Mathematics CBSE Solutions.

Triangles

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Answer

Two polygons of the same number of sides are similar if

  1. All the corresponding angles are equal.
  2. All the corresponding sides are in the same ratio (or proportion).

In quadrilaterals ABCD and PQRS,

⇒ ABPQ=31.5=3015\dfrac{AB}{PQ} = \dfrac{3}{1.5} = \dfrac{30}{15} = 2,

⇒ BCQR=31.5=3015\dfrac{BC}{QR} = \dfrac{3}{1.5} = \dfrac{30}{15} = 2,

⇒ CDRS=31.5=3015\dfrac{CD}{RS} = \dfrac{3}{1.5} = \dfrac{30}{15} = 2,

⇒ ADSP=31.5=3015\dfrac{AD}{SP} = \dfrac{3}{1.5} = \dfrac{30}{15} = 2.

So,

⇒ABPQ=BCQR=CDRS=ADSP\Rightarrow \dfrac{AB}{PQ} = \dfrac{BC}{QR} = \dfrac{CD}{RS} = \dfrac{AD}{SP}.

⇒ Corresponding sides are in proportion.

But ∠A ≠ ∠P; ∠B ≠ ∠Q

Thus, corresponding angles are not equal.

Hence, quadrilateral ABCD is not similar to quadrilateral PQRS.

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