1.

in the adjoining figure, AD is a median of ∆ ABC and DE || BA . show that BE is also a median of ∆ ABC​

Answer»

GIVEN :-

  • In ∆ ABC, AD is a median and DE || BA.

To Prove :-

  • BE is also a median of ∆ ABC. (That means require to prove E is the midpoint of AC.)

Concept Used :-

  • Converse of Midpoint theorem - states that "if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.

  • Median - Median is the line segment from a vertex to the midpoint of the opposite side. 

Proof :-

Given that

  • In ∆ ABC,

  • AD is median

  • ⇛ D is the midpoint of BC.

Now,

Again,

  • In ∆ ABC,

  • D is the midpoint of BC. [ Proved above ]

  • and DE || BC [ Given ]

So,

By Converse of Midpoint Theorem,

  • E is the midpoint of AC.

Hence,

  • BE is median of ∆ ABC.

Additional Information :-

Midpoint Theorem -

states that “The line segment in a triangle JOINING the midpoint of two sides of the triangle is SAID to be parallel to its third side and is also half of the length of the third side.”


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