"DO NOT SEND ANY LINKS".
Answer the 1st question.
Q.1. In the given figure, PA$\perp$AB; PA = QB. If PQ intersects AB at M, show that M is the mid-point of both AB and PQ.

We know that in triangles PAM and BQM,
PA=QB (GIVEN)
ANGLES PAM=BQM (GIVEN)
ANGLES AMP=QMB ( VERTICALLY OPPOSITE ANGLES)
By AAS, Triangles PAM=BQM.
By CPCT, AM=BM
      and      PM=QM.
Therefore, M is the midpoint of both lines.