CBSE Class 9 Answered
ABCD is a trapezium in which AB||CD and AD
= BC
Show that:
(a) A
= B
(b) C = D
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
(a)
Const: Draw EC || AD
Proof:
AD = CE (Opposite sides of parallelogram AECD)
However, AD = BC (Given)
Therefore, BC = CE
CEB = CBE (Angle opposite to equal sides are also equal)
Consider parallel lines AD and CE. AE is the transversal line for them.
A + CEB = 180º (Angles on the same side of transversal)
A + CBE = 180º (Using the relation CEB = CBE) ... (1)
However, ∠ABC + ∠CBE = 180º (Linear pair angles) ... (2)
From equations (1) and (2), we obtain
DAB = ABC
ie, A=B
(b)
Construction : Draw BE||AD
Proof : ABED is a parallelogram
Answered by | 04 Jun, 2014, 03:23: PM
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