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

In the given figure, M is the mid-point of AB and DE, whereas N is mid-point of BC and DF. Show that : EF = AC. Mid-point Theorem, Concise Mathematics Solutions ICSE Class 9.

Mid-point Theorem

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Answer

By mid-point theorem,

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

In △ EDF,

M is the mid-point of ED and N is the mid-point of DF.

∴ MN = 12EF\dfrac{1}{2}EF (By mid-point theorem)

⇒ EF = 2MN ………….(1)

In △ ABC,

M is the mid-point of AB and N is the mid-point of BC.

∴ MN = 12AC\dfrac{1}{2}AC (By mid-point theorem)

⇒ AC = 2MN ………….(2)

From (1) and (2), we get :

⇒ EF = AC.

Hence, proved that EF = AC.

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