Q18 of 93 Page 6

In the figure, show that AB || EF.

     ∠ABC = 70° 
   ∠BCD = ∠BCE + ∠ECD = 30° + 40° = 70°
=>   ∠ABC = ∠BCD = 70°
Hence, interior alternate angles are equal 
=>   AB || CD 
Now ∠FEC + ∠ECD = 140° + 40° = 180°
But these angles are consecutive interior angles 
  =>  CD || EF
Also CD || AB
  ... AB || EF

More from this chapter

All 93 →
16 In quadrilateral ABCD, AB || CD and AD || BC. Prove that ∠ABC = ∠ADC.
 17 Ray OE bisects ∠AOB and OF is the ray opposite OE. Show that ∠FOB =∠FOA.
 19 Find the value of x in the following figures if
(a) AB || CD
(b) AB || CD and BC || DE
(c) AB || CD and BC || ED
(d) BA || CD
   
(a)                              (b)

(c)                          (d) 20 Rays OA, OB, OC, OD and OE have the common end point O. Show that ∠AOB + ∠BOC+ ∠COD + ∠DOE + ∠EOA = 360°.