If PQ QR - YZ ZX and QR PR - ZX YX - then nbsp- PQR - YZX-RPQ - YZX-PQR - XYZ-They are not similar-

The correct option is A PQR ∼ YZX PQ QR = YZ ZX ⇒PQ YZ = QR ZX ———– I QR PR = ZX YX ⇒QR ZX = PR YX ———–II From I and II, PQ YZ = QR ZX = PR YX ∴ PQR ∼ YZX by S ...

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Byju's Answer

Standard VIII

Mathematics

SSS similarity

If PQ QR = YZ...

Question

If $\frac{P Q}{Q R} = \frac{Y Z}{Z X}$ and $\frac{Q R}{P R} = \frac{Z X}{Y X}$ , then

$△ P Q R \sim △ Y Z X$

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$△ R P Q \sim △ Y Z X$

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$△ P Q R \sim △ X Y Z$

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They are not similar

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Solution

The correct option is A
$△ P Q R \sim △ Y Z X$

$\frac{P Q}{Q R} = \frac{Y Z}{Z X}$

$\Rightarrow \frac{P Q}{Y Z} = \frac{Q R}{Z X}$ ----------- I

$\frac{Q R}{P R} = \frac{Z X}{Y X}$

$\Rightarrow \frac{Q R}{Z X} = \frac{P R}{Y X}$ -----------II

From I and II,

$\frac{P Q}{Y Z} = \frac{Q R}{Z X} = \frac{P R}{Y X}$

$∴ △ P Q R \sim △ Y Z X$ by SSS axiom.

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Similar questions

In △ PQR, if QS is the angle bisector of ∠ Q, then show that \frac{A (△ PQR)}{A (△ QRS)} = \frac{PQ}{QR} .

If $\frac{P Q}{Q R} = \frac{Y Z}{Z X}$ and $\frac{Q R}{P R} = \frac{Z X}{Y X}$ , then

a. $△ P Q R \sim △ Y Z X$
b. $△ R P Q \sim △ Y Z X$
c. $△ P Q R \sim △ X Y Z$
d. They are not similar
$[1]$