Question

20. In the given figure show that
(a) AB|| CD
(b) CD || EF
(c) ABII EF

Answer 1

Given, Angle B = 62⁰

Angle BCE = 30⁰

Angle ECD = 32⁰

Angle FEC = 148⁰

i) To prove -- AB II CD

Angle BCD = BCE + ECD = (30 + 32)⁰

= 62⁰

Now, Angle B = Angle BCD

but, Angle B and Angle BCD are alternate interior angles on opposite sides of transversal BC.

=> AB II CD ---------- (1)

ii) To prove -- EF II CD

Angle E + Angle ECD = 148⁰ + 32⁰

= 180⁰

Also, Angle E and Angle ECD are co interior angles ( sum of co-interior angles = 180⁰) on same side of transversal.

=> EF II CD ------- (2)

iii) To prove --- AB II EF

From (1) and (2),

AB II CD and EF II CD,

=> AB also parallel to EF.