Question

In the given figure, M is mid-point of AB and DE, whereas N is mid-point of BC and DF.
Show that: EF = AC.

Answer 1

ln ΔEDF,
M is the mid-point of AB and N is the mid-point of DE.
⇒ MN = `1/2`EF            ...( Mid-point theorem )
⇒ EF = 2MN                 ...(i)

ln ΔABC,
M is the mid-point  of AB and N is the mid-point of BC,
⇒ MN = `1/2`AC              ....( Mid-point theorem )

⇒ AC =2MN                     ....(ii)
From (i) and (ii), we get
⇒ EF = AC