Question

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

Answer 1

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.”

Answer 2

ㅤㅤㅤㅤ❈Question:-

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

ㅤㅤㅤㅤ✲Given :-

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

ㅤㅤㅤㅤ✯To Prove :-

• BE is also a median of ∆ ABC.

ㅤㅤㅤㅤ✾Solution:-

In ΔABC

➟It is given that DE || AB.

➟We know that D is the midpoint of BC ㅤㅤㅤㅤㅤㅤㅤ_______based on mid point theorem

• E is the mid point of AC

$\underline{ \sf{So \: we \: know that \: BE \: is \: the \: median \: of \: \triangle \: ABC \: drawn \: through \: B}}$

Hence Proved that BE is also a median of ∆ ABC.

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Learn More:-✔

$\underline{ \boxed{ \rm{ \red{What \: is \: mid \: point \: theorem?}}}}$

• The 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.”

$\underline{ \boxed{ \mathrm{ \pink{Converse \: of \: mid \: point \: theorem?}}}}$

• The line drawn through the midpoint of one side of a triangle, parallel to another side bisects the third side.