question_answer

Match the following.      

Column-l	Column-ll
(P) In \[\Delta \,ABC\] and \[\Delta \,PQR\] \[\frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P\]\[\Rightarrow \] \[\Delta ABC\tilde{\ }\Delta PQR\]	(1) AA similarity criterion
(Q) In \[\Delta ABC\] and \[\Delta PQR\] \[\angle A=\angle P,\angle B=\angle Q\] \[\Rightarrow \]   \[\Delta \,ABC\tilde{\ }\Delta PQR\]	(2) SAS similarity criterion
(R) In \[\Delta \,ABC\] and \[\Delta \,PQR\] \[\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}\] \[\Rightarrow \]   \[\Delta \,ABC\tilde{\ }\Delta PQR\]	(3) SSS similarity criterion
(S)  In \[\Delta \,ABC\], \[DE||BC\] \[\Rightarrow \]  \[\frac{AD}{BD}=\frac{AE}{CE}\]	(4) BPT

A)            (P)\[\to \](1), (Q)\[\to \](2), (R)\[\to \] (3), (S)\[\to \](4)

B)  (P)\[\to \](2), (Q)\[\to \](1), (R)\[\to \](3), (S)\[\to \](4)

C)  (P)\[\to \](4), (Q)\[\to \](2). (R)\[\to \](1), (S)\[\to \](3)

D)  (P)\[\to \](3),(Q)\[\to \](1),(R)\[\to \](4),(S)\[\to \](2)

Correct Answer: B

Solution :

(P) Given: \[\frac{AB}{PQ}=\frac{AC}{PR},\,\,\angle A=\angle P\] \[\therefore \] \[\angle A\] is containing the sides AB and AC and \[\angle P\]is containing the sides PQ and PR. \[\therefore \]   \[\Delta ABC\tilde{\ }\Delta PQR\]         (By SAS criteria) (Q) Given:  \[\angle A=\angle P,\,\,\,\angle B=\angle Q\]  \[\therefore \]   \[\Delta ABC\tilde{\ }\,\Delta PQR\]     (By AA criteria) (R) Given:  \[\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}\] \[\because \] Sides of the \[\Delta ABC\]and \[\Delta PQR\] are in proportion \[\therefore \]\[\Delta ABC\tilde{\ }\Delta PQR\]         (By SSS criteria) (S) Given,\[DE||BC\]             \[\therefore \]   \[\frac{AD}{BD}=\frac{AE}{EC}\]              (By B.P.T.)