If PQ QR - YZ ZX and QR PR - ZX YX - then a- PQR - YZXb- RPQ - YZXc- PQR - XYZd- They are not similar-1-

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 SSS axiom. Correct nbsp; Opt ...

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Standard X

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

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
$[1]$

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Solution

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

$\Rightarrow \frac{P Q}{Y Z} = \frac{Q R}{Z X}$ ----------- 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.
Correct Option: a
$[1]$

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If PQQR=YZZX and QRPR=ZXYX , then a. △PQR∼△YZX b. △RPQ∼△YZX c. △PQR∼△XYZ d. They are not similar [1]

PQQR=YZZX ⇒PQYZ=QRZX ----------- I QRPR=ZXYX ⇒QRZX=PRYX -----------II From I and II, PQYZ=QRZX=PRYX ∴△PQR∼△YZX by SSS axiom. Correct Option: a [1]

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
$[1]$