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keshav kumar
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Asked: 2023-03-31T03:19:27+00:00 In:

In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ∆ ABC ≅ ∆ DEF.

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In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ∆ ABC ≅ ∆ DEF.

Define the opposite angles of quadrilateral.
To prove the opposite angles of quadrilateral are supplementary.
Class 9th Maths Important Question Answer, Session 2023-2024.
Quadrilaterals, EXERCISE 8.1, Page No: 147, Questions No:11.

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    1. Best Answer
      In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ∆ ABC ≅ ∆ DEF.

      (i) In ABED, AB = DE [∵ Given]
      AB ∥ DE [∵ Given]
      Hence, ABED is a parallelogram.

      (ii) In BEFC, BC = EF [∵ Given]
      BC ∥ EF [∵ Given]
      Hence, BEFC is a parallelogram.

      (iii) In ABED,
      AD = BE …(1) [∵ ABED is a parallelogram]
      AD ∥ BE …(2) [∵ ABED is a parallelogram]
      In BEFC,
      BE = CF …(3) [∵ ABED is a parallelogram]
      BE ∥ CF …(4) [∵ ABED is a parallelogram]
      From (2) and (4), we have
      AD ∥ CF …(5)
      From (1) and (3), we have
      AD = CF …(6)
      (iv) In ACFD,
      AD = CF [∵ From (6)]
      AD ∥ CF [∵ From (5)]
      Hence, ACFD is a parallelogram
      (v) In ACFD,
      AC = DF . [∵ ACFD is a parallelogram]

      (vi) In ΔABC and ΔDEF
      AB = DE [∵ Given]
      AC = DF [∵ Proved above]
      BC = EF [∵ Given]
      Hence, ΔABC ≅ ΔDEF [∵ SSS Congruency rule]

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