Question

converse mid point theorem​

Answer 1

Answer:

Midpoint Theorem Converse

The Midpoint Theorem works conversely, too: if you draw a line parallel to a side of a triangle through one side's midpoint, it will automatically (magically?) intersect the midpoint of the remaining side.

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Answer 2

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

Converse of Midpoint Theorem Proof

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

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

Converse of Midpoint Theorem

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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.

The converse of MidPoint Theorem

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”.