Question

In the given figure,

$XY||QR$, $XZ||PR$ and $YZ||PQ$.
Which of the following correct?

• A. $△XYZ\sim △RQP$
• B. $△XYZ\sim △PQR$
• C. $\angle X=\angle P$
• D. $\angle Y=\angle R$

Answer 1

The correct option is A $△XYZ\sim △RQP$

In the above figure, lets do some construction bny extending all the sides of $△PQR$ meeting at sides of $△XYZ$.

So, we can see that
$\angle Y=\angle Q\text{(first corresponding and then alternate as shown by black color)}$.
Similarly,
$\angle X=\angle R\text{and}\angle Z=\angle P\text{(shown by red and green color respectively)}$
Hence, $△XYZ$~$△RQP$ (AAA)
So, option $\left(a\right)$ correct.