CBSE Class 9 Answered

(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