Question

State and explain converse of The midpoint theorem.​

Answer 1

$\boxed{\huge\underline{\mathscr\purple{♡ANSWER♡}}}$

→ The converse of the 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”.

FOR PROOF # REFER TO ATTACHMENT

HOPE IT HELPS ‼️

Answer 2

Question:-

State and explain "Converse of the Mid Point Therom.

Answer:-

Statement:

☛ The line drawn through the mid-point of one side of a triangle parallel to the base of a triangle bisects the third side of the triangle.

Proof of Converse Of The Mid Point Therom:

Given: In triangle PQR, S is the mid-point of PQ and ST ∥ QR

To Prove: T is the mid-point of PR.

Construction: Draw a line through R parallel to PQ and extend ST to U.

Proof: ST ∥ QR(given)

So, SU ∥ QR

PQ∥ RU (construction)

Therefore, SURQ is a parallelogram.

SQ = RU (Opposite sides of parallelogram)

But SQ = PS (S is the mid-point of PQ)

Therefore, RU = PS

In △PST and △RUT

∠1 =∠2 (vertically opposite angles)

∠3 =∠4 (alternate angles)

PS = RU (proved above)

∴ △PST ≅ △RUT (by AAS criteria)

Therefore, PT = RT

T is the mid-point of PR.