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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(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]