In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.
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16
Answer:
In ABED,
- it is a parallelogram....one pair of opposite sides is equal and parallel...... from 2&3
- AB = ED....given
- AB || ED.....given
- therefore,
- AD = BE & AD || BE......opposite sides of a parallelogram are equal and parallel......since ABED is a parallelogram.....from 1
- AC || DF........ give
- AC = DF........give
- ACFD is a parallelogram......from 6&7....one pair of opposite sides is equal and parallel
- therefore,
- AD = CF & AD || CF......from 8
- BCFE is a rectangle as one pair of opposite sides is equal and parallel.......5&8
- therefore,
- BC = EF & BC || EF....opposite sides of rectangle are equal and parallel.
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Answered by
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
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