ABCD is square M is midpoint on AB such that AM=MB P and Q are points on side AD and - Maths - Areas of Parallelograms and Triangles

Question

ABCD is square M is midpoint on AB such that AM=MB P and Q are
points on side AD and extended CB such that CM perdicular PQ show
that at CPM =at CQM

Varun.Rawat · Accepted Answer

In ∆PAM and ∆QBM,∠PMA = ∠QMB    Vertically opposite angles      AM = MB             M is the mid point of AB∠PAM = ∠QBM     90° each⇒∆PAM ≅ ∆QBM   ASA⇒PM = QM         CPCTIn ∆CPM and ∆CQM,       PM = QM           Proved above∠CMP = ∠CMQ    90° each      CM = CM           Common⇒∆CPM ≅∆CQM  SAS⇒ar∆CPM = ar∆CQM    Congruent ∆'s have equal areas

ABCD is square M is midpoint on AB such that AM=MB P and Q are points on side AD and extended CB such that CM perdicular PQ show that at CPM =at CQM