question_answer

If in two triangles DEF and PQR, \[\angle D=\angle Q\] and   then which of the following is not true? (NCERT EXEMPLAR)

A) \[\frac{EF}{PR}=\frac{DF}{PQ}\]

B) \[\frac{DE}{PQ}=\frac{EF}{RP}\]

C) \[\frac{DE}{QR}=\frac{DF}{PQ}\]

D) \[\frac{EF}{RP}=\frac{DE}{QR}\]

Correct Answer: B

Solution :

[b] Given, in \[\Delta DEF\] and \[\Delta PQR\],

\[\angle D=\angle Q,\,\,\,\angle R=\angle E\]

\[\therefore \,\,\,\Delta DEF\tilde{\ }\Delta QRP\](By AA similarity criterion)

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\angle F=\angle P\]

(Corresponding angles of similar triangles)

\[\therefore \,\,\,\,\,\,\,\,\,\,\frac{DF}{QP}=\frac{ED}{RQ}=\frac{FE}{PR}\]