Math, asked by monukumarmonukumar93, 8 months ago

In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF. ​

Attachments:

Answers

Answered by pmd29
16

Answer:

In ABED,

  1. it is a parallelogram....one pair of opposite sides is equal and parallel...... from 2&3
  2. AB = ED....given
  3. AB || ED.....given
  4. therefore,
  5. AD = BE & AD || BE......opposite sides of a parallelogram are equal and parallel......since ABED is a parallelogram.....from 1
  6. AC || DF........ give
  7. AC = DF........give
  8. ACFD is a parallelogram......from 6&7....one pair of opposite sides is equal and parallel
  9. therefore,
  10. AD = CF & AD || CF......from 8
  11. BCFE is a rectangle as one pair of opposite sides is equal and parallel.......5&8
  12. therefore,
  13. BC = EF & BC || EF....opposite sides of rectangle are equal and parallel.

pls mark my answer brainlist

Answered by rajviparmar9045
13

Answer:

here's the answer ⬇

Step-by-step explanation:

Given In figure AB || DE and AC || DF, also AB = DE and AC = D

To prove BC ||EF and BC = EF

Proof: In quadrilateral ABED, AB||DE and AB = DE

So, ABED is a parallelogram. AD || BE and AD = BE

Now, in quadrilateral ACFD, AC || FD and AC = FD …..(i)

Thus, ACFD is a parallelogram.

AD || CF and AD = CF …(ii)

From Eqs. (i) and (ii), AD = BE = CF and CF || BE …(iii)

Now, in quadrilateral BCFE, BE = CF

and BE||CF [from Eq. (iii)]

So, BCFE is a parallelogram. BC = EF and BC|| EF .

✅Hence proved

Similar questions