Lines & Angle problem

omair_bba wrote:Hi, Below Q is not from any OG.

Q: Concerning the figure below, if a=b, which of the following statements must be true?

(I) c=d , (II) f & k are parallel. , (III) m & f are perpendicular.

A) None
B) I only
C) I & II only
D) I & III only
E) I,II & III





Please explain answer too !

Thankx...

From the figure given a+c=180 and b+d=180. Since a=b, we can say that c=d. I'm not sure if the II and III MUST BE TRUE. IMO B

But what else I should know to eliminate II & III with surety ?

Dear Omair,

I have redrawn the figure you posted in such a way that it satisfies the given condition of a=b.

You need to imagine possibilities to prove option (II) and Option (III) wrong.

You can see in the following figure, 'f' & 'k' are neither parallel nor 'm' & 'f' are perpendicular.
It also satisfies all the given conditions.

So, we can conclude that, only condition (I) is true as a,c & b,d form a linear pair. Thus, a=b => c=d

Ans: Option B