Long Answer TypeIn ∆ABC and ∆DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, Band C are joined to vertices D, E and F respectively (see figure). 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. [CBSE 2012
Short Answer TypeABCD is a trapezium in which AB || CD and AD = BC (see figure): Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC = ∆BAD
(iv) diagonal AC = diagonal BD.
[Hint. Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]
Long Answer TypeShort Answer TypeLong Answer TypeShort Answer TypeGiven ∆ABC, lines are drawn through A, B and C parallel respectively to the sides
BC, CA and AB forming ∆PQR. Show that BC = 
Proof: ∵ AQ || CB and AC || QB
∴ AQBC is a parallelogram
∴ BC = QA ...(1)
| Opposite sides of a ||gm
∵ AR || BC and AB || RC
∴ ARCB is a parallelogram
∴ BC = AR ...(2)
| Opposite sides of a ||gm
From (1) and (2),
QR.Long Answer TypeABCD is a trapezium in which AB || CD and AD = BC. Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC ≅ ∆BAD.
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