Converse of Midpoint Theorem | Proof of Converse of Midpoint Theorem

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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.

Converse of Midpoint Theorem Proof

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

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

Converse of Midpoint Theorem

Proof:

            Statement

          Reason

1. SU ∥ QR and SU = (frac{1}{2})QR.

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.

9th Grade Math

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