Question

what is converse of mid point theorem ? and also prove​

Answer 1

A converse of a theorem is a statement formed by interchanging what is given in a theorem and what is to be proved. For example, the isosceles triangle theorem states that if two sides of a triangle are equal then two angles are equal.

GIVEN: ABC is a triangle

AD =BD

DE PARALLEL TO BC

TO PROVE: EA=EC

CONSTRUCTION: Draw CF parallel to AB

PROOF: In triangle EDA and EFC

DE parallel to BC

Hence DB = and parallel to FC

Therefore BDEF is a parallelogram ....

hence it is proved....

I HOPE IT HELPS U...

TQ.....

PLZZ MARK MY ANS AS BRAINLIST....

Answer 2

Given: In ∆PQR, S is the midpoint of PQ, and ST is drawn parallel to QR.

To prove: ST bisects PR, i.e., PT = TR.

Construction: Join SU where U is the midpoint of PR.

Proof:

           Statement

         Reason

1. SU ∥ QR and SU = 12QR.

1. By Midpoint Theorem.

2. ST ∥QR and SU ∥ QR.

2. Given and statement 1.

3. ST ∥ SU.

3. Two lines parallel to the same line are parallel themselves.

4. ST and SU are not the same line.

4. From statement 3.

5. T and U are coincident points.

5. From statement 4.

6. T is the midpoint of PR (Proved).

6. From statement 5.