Question

4. In the given figure, prove that AB || CD

Answer 1

Step-by-step explanation:

Draw a line KH passing through the point F which is parallel to both AB and CD 

We know that KF∥CD and FG is a transversal

from the figure we know that ∠KFG and ∠FGD are alternate angles

So we get

∠KFG=∠FGD=ro...(i)

We also know that AE∥KF and EF is a transversal

from the figure we know that ∠AEF and ∠KFE are alternate angles

So we get

∠AEF+∠KFE=180o

By substituting the values we get

po+∠KFE=180o

∠KFE=180o−po....(ii)

By adding both the equations (i) and (ii) we get

∠KFG+∠KFE=180o−po+ro

from the figures ∠KFG+∠KFE can be written as ∠EFG

∠EFG=180o−po+ro

We know that ∠EFG=qo

qo=180o−po+ro

It can be written as

p+q−r=180o

Therefore it is proved that p+