Question

Point a and b lie on same side of line xy. if ad perpendiculer to xy and be perpendicular to xy and c is midpoint of ab prove cd=ce​

Answer 1

CD = CE by CPCT rule.

Constructing a perpendicular as C TO DE at Z.

In the figure, the transversal AB will make an equal transversal with AD, CZ, BE

Thus, it will also make an equal intercept with DE .

Hence, in ΔCDZ and ΔCEZ

DZ = DE

∠CZD = ∠CZE ( By construction )

CZ = CZ ( Common Side )

Therefore, ΔCDZ ≅ ΔCEZ ( By SAS congruency )

SO CD = CE by the CPCT rule.

Answer 2

∆CDZ = ∆CEZ {BY SAS}

CD = CE {C.P.C.T}