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(B) $1$. In $\Delta ABC$ and $\Delta PQR$,if $\angle A = \angle P$ and $\angle C = \angle Q$,then by $AA$ similarity,$\Delta ABC \sim \Delta PRQ$. Thu

Vedclass · Accepted Answer

$(1-d), (2-b), (3-c), (4-a)$

Vedclass · Answer

(B) $1$. In $\Delta ABC$ and $\Delta PQR$,if $\angle A = \angle P$ and $\angle C = \angle Q$,then by $AA$ similarity,$\Delta ABC \sim \Delta PRQ$. Thus,$(1-d)$.$2$. In $\Delta ABC$ and $\Delta PQR$,if $\frac{AB}{QR} = \frac{BC}{PQ}$ and $\angle B = \angle Q$,then by $SAS$ similarity,$\Delta ABC \sim \Delta RQP$. Thus,$(2-a)$.$3$. In $\Delta ABC$ and $\Delta PQR$,if $\frac{AB}{PQ} = \frac{BC}{PR} = \frac{CA}{QR}$,then by $SSS$ similarity,$\Delta ABC \sim \Delta PQR$. Thus,$(3-c)$.$4$. In $\Delta ABC$ and $\Delta PQR$,if $\frac{AB}{PQ} = \frac{CA}{PR}$ and $\angle A = \angle P$,then by $SAS$ similarity,$\Delta ABC \sim \Delta QPR$. Thus,$(4-b)$.Therefore,the correct matching is $(1-d), (2-a), (3-c), (4-b)$. Note: The provided options seem to have a slight mismatch in the sequence,but based on standard similarity criteria,the correct pairing is $(1-d), (2-a), (3-c), (4-b)$.

Part $I$	Part $II$
$1.$ In $\Delta ABC$ and $\Delta PQR, \angle A \cong \angle P$ and $\angle C \cong \angle Q$	$a.$ Correspondence $ABC \leftrightarrow RQP$ is a similarity.
$2.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{QR} = \frac{BC}{PQ}$ and $\angle B \cong \angle Q$	$b.$ Correspondence $ABC \leftrightarrow QPR$ is a similarity.
$3.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{PQ} = \frac{BC}{PR} = \frac{CA}{QR}$	$c.$ Correspondence $ABC \leftrightarrow PQR$ is a similarity.
$4.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{PQ} = \frac{CA}{PR}$ and $\angle A \cong \angle P$	$d.$ Correspondence $ABC \leftrightarrow PRQ$ is a similarity.

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