Which of the following is NOT a property of similar triangles?

Question

Question

This question was previously asked in

RRB Group D 30 Aug 2022 Shift 3 Official Paper

Ratio of areas of two similar triangles = Ratio of squares of corresponding segments obtained by corresponding angle bisectors.
Ratio of areas of two similar triangles = Ratio of squares of corresponding medians
Ratio of areas of two Similar triangles = Ratio of squares of corresponding altitudes
Ratio of areas of two similar triangles= Ratio of corresponding segments obtained by corresponding angle bisectors.

Answer 1

Calculations:

In △ABC and △PQR

⇒ ∠A = ∠P

⇒ or 1/2∠A = 1/2∠P

⇒ ∠1 = ∠2

⇒ and, ∠B = ∠Q

hence, △ABC ~ △PQR

⇒ \(\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}\)

Now,

⇒ \(\frac{ar(ABC)}{ar(PQR)}=\frac{\frac{1}{2}AL\times BC}{\frac{1}{2}PM\times QR}=\frac{AL\times AL}{PM\times PM}=\frac{AL^2}{PM^2}\)

⇒ Hence, Option 4 is incorrect