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.)You need to login to perform this action.
You will be redirected in
3 sec