Question

converse of midpoint theorem with proof​

Answer 1

Step-by-step explanation:

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

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