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Prove that any line segment drawn from the vertex of a triangle to the base is bisected by the line segment joining mid-points of the other sides of the triangle.

Answer 1

Hey mate!

Here's ur answer dear:-)

GIVEN : ABC is a triangle, in which D is the mid - point of AB and E is the mid-point of AC. AL is a straight line that intersects DE at M and BC at L.

TO PROVE : DE bisects AL.

PROOF : Since D and E are the mid points of the sides AB and AC of △ABC, then 

✔   DE || BC      .....(1)     [ Mid point theorem, the line segment joining the mid points of two sides of a triangle is parallel to the third side and is half of it. ]

Since DE || BC, then DM || BL.   [as DM is a part of DE and BL is a part of BC] .

In △ ABL, we have D is the mid point of AB and DM || BL , then M must be the mid point of AL.   [CONVERSE OF MID POINT THEOREM, the line drawn through the mid-point of one side of a triangle,parallel to another side, intersects the third side at its mid-point.]

⇒AM = ML

⇒DE bisects AL.

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Hope it helps!☺☺☺
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Answer 2

Hiii......Frnd....

Good morning☺️......

Here is your answer

GIVEN-:✅ABC is a triangle,in which D is the mid-point of AB and E is mid-point of AC.AL is a starlight Line that interesects DE at M and BC at L.

To prove-:
✔️ DE bisects AL.

PROOF-: Since D and E is the mid-points of the sides AB and AC of triangle ABC,
Then

DE || BC ........(1). [ Mid-point theorem]

Since DE || BC , then DM || BL. [ As DM is a part of DE and BL is a part of BC]

In triangle ABL, we have D is mid-point of AB and DM || BL, the M must be the mid-point of AL. [converse of Mid-point Theorem]

=> AM = ML

=> DE bisects AL

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Hope it help you✌️✌️........

Have a nice day☺️