9th Class
Mathematics
Quadrilaterals
Question Bank
Quadrilaterals
question_answer
D and E are the mid-points of the sides AB and AC, respectively of \[\Delta ABC.DE\]is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
A)\[\angle DAE=\angle EFC\]
B) AE = EF
C) DE = EF
D) \[\angle ADE=\angle ECF\]
Correct Answer:
C
Solution :
We have produced DE to F such that DE = EF ?(i) In\[\Delta \Alpha DE\]and \[\Delta CFE,\] AE = CE [\[\therefore \]E is the mid-point of AC] \[\angle AED=\angle CEF\][Vertically opposite angles] DF = FE [By (i)] \[\therefore \]\[\Delta ADE\cong \Delta CFE\] [By SAS congruency] \[\therefore \]\[AD=CF\]and \[\angle ADE=\angle CFE\] [By CPCT] This show that alternate interior angles are equal. Thus, \[AD||CF\] Therefore, the additional information which we need is DE = EF