Question

If $\frac{PQ}{QR}=\frac{YZ}{ZX}$ and $\frac{QR}{PR}=\frac{ZX}{YX}$ , then

• A. $△PQR\sim △YZX$
• B. $△RPQ\sim △YZX$
• C. $△PQR\sim △XYZ$
• D. They are not similar

Answer 1

The correct option is A

$△PQR\sim △YZX$

$\frac{PQ}{QR}=\frac{YZ}{ZX}$

$\Rightarrow \frac{PQ}{YZ}=\frac{QR}{ZX}$ ----------- I

$\frac{QR}{PR}=\frac{ZX}{YX}$

$\Rightarrow \frac{QR}{ZX}=\frac{PR}{YX}$ -----------II

From I and II,

$\frac{PQ}{YZ}=\frac{QR}{ZX}=\frac{PR}{YX}$

$\therefore △PQR\sim △YZX$ by SSS axiom.