Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

Q: 5  In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. \small 8.31). Show that the line segments AF and EC trisect the diagonal BD. 

  

Answers (1)

best_answer

Given: In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively

To prove: the line segments AF and EC trisect the diagonal BD.

Proof : In quadrilateral ABCD,     

  AB=CD                             (Given)

   \frac{1}{2}AB=\frac{1}{2}CD

\Rightarrow AE=CF         (E and F are midpoints of AB and CD)

In quadrilateral AECF,     

 AE=CF                  (Given)

 AE || CF               (Opposite sides of a parallelogram)

Hence,  AECF is a parallelogram.

In \triangle DCQ,

 F is the midpoint of DC.      (given )

 FP || CQ           (AECF  is a parallelogram)

By converse of midpoint theorem,

 P is the mid point of DQ.      

 DP= PQ....................1

Similarly,

 In \triangle ABP,

 E is the midpoint of AB.      (given )

 EQ || AP          (AECF  is a parallelogram)

By converse of midpoint theorem,

 Q is the midpoint of PB.      

 OQ= QB....................2

From 1 and 2, we have 

DP = PQ = QB.

Hence, the line segments AF and EC trisect the diagonal BD.

 

 

 

 

 

Posted by

mansi

View full answer

Similar Questions

Trending Articles/News

anam-khan

Board Exam Date 2025 Live: Bihar Class 10, 12 model papers out, time table soon; updates on CBSE, UP
anam-khan

CBSE Class 10 board exams from February 15 to March 18; download date sheet 2025 PDF

Latest Question