Question

prove converse of mid point theorem

Answer 1

Given : P is the mid point of AB
PQllBC
To prove : Q is the mid point.
Construction : From point Q draw BE ll AB .
Proof : QE ll AB. ( by construction)
PQ ll BC. ( given )
Thus, PBEQ is a parallelogram.

PB = QE. ...(I) ( opp. Sides of parallelogram )
In triangles APQ and QCE,
AP = QE. ( by eq I)
Angle 1= 2
Angle 3= 4. (corresponding angles)

So, triangle AQP is congruent to trainable QCE. ( by AAS)
And so by CPCT,
AQ = QC
Hence proved

Answer 2

Hi friend..
See the attached file

I hope it will help you
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