Column - I | Column - II | ||
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 \[\Delta ABC\], \[DE||BC\] \[\Rightarrow \,\frac{AD}{DB}=\frac{AE}{EC}\] | 4. | BPT |
A) P-1, Q-2, R-3, S-4
B) P-2, Q-1, R-3, S-4
C) P-4, Q-3, R-2, S-1
D) P-4, Q-3, R-2, S-4
Correct Answer: B
Solution :
(P) |
Given, \[\frac{AB}{PQ}=\frac{AC}{PR}\], |
\[\angle A=\angle P\] |
\[\because\] \[\angle A\] is containing the sides AB and AC and is containing the sides PQ and PR. |
\[\therefore \,\,\,\Delta ABC-\Delta PQR\] |
[by SAS criterion of similarity] |
(Q) |
Given, \[\angle A=\angle P,\,\angle B=\angle Q\] |
\[\therefore \Delta ABC-\angle PQR\] |
[by AA criterion of similarity] |
(R) |
Given, |
\[\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}\] |
\[\because\] Sides of the \[\Delta ABC\] and \[\Delta PQR\]are in proportion |
\[\therefore \Delta ABC-\Delta PQR\] |
[by SSS criterion of similarity] |
(S) |
Given \[DE\,|\,\,|\,\,BC\] |
\[\therefore \,\,\,\,\frac{AD}{BD}=\frac{AE}{EC}\] [by BPT] |
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