Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively .Show that
quadrilateral ABED is a parallelogram
Given: Δ ABC and Δ DEF,
AB = DE, AB ∥ DE, BC = EF and BC ∥ EF
To prove: ABED is a parallelogram
Proof:
Given that AB = DE and AB ∥ DE.
⇒ One pair of opposite sides are equal and parallel to each other
∴ ABED is a parallelogram
Hence proved
Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to
vertices D, E and F respectively. Show that
(ii) quadrilateral BEFC is a parallelogram
Given that BC = EF and BC ∥ EF.
⇒One pair of opposite sides are equal and parallel to each other
∴ BEFC is a parallelogram
Hence proved
Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to
vertices D, E and F respectively. Show that
(iii) AD ∥ CF and AD = CF
From part(i), we proved that
ABED is a parallelogram
So, AD = BE and AD ∥ BE
From part(ii) , we proved that
BEFC is a parallelogram
So, BE = CF and BE ∥ CF
Hence From (1) & (2)
∴ AD = CF and AD ∥ CF
Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to
vertices D, E and F respectively. Show that
(iv) quadrilateral ACFD is a parallelogram
In part (iii) we proved that
AD = CF and AD ∥ CF
⇒One pair of opposite sides are equal and parallel to each other
∴ ACFD is a parallelogram
Therefore, quadrilateral ACFD is a parallelogram.
Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to
vertices D, E and F respectively. Show that
(v) AC = DF
From part(iv), ACFD is a parallelogram
So, AC = DF
Hence proved
Ex 8.1, 11
In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to
vertices D, E and F respectively .Show that
(vi) Δ ABC ≅ Δ DEF.
In ΔABC and ΔDEF,
AB = DE
BC = EF
AC = DF
∴ ΔABC ≅ ΔDEF

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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