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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.
Solution
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
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