Finding proof for triangle?

Angle  DWL = Angle CWK    [they are the same angle]
And angles  WLD  and WKC are both right angles   [all right angles are congruent ]

Then, by Angle-Angle congruency, ΔWKC  is similar to ΔWLD

Thus

DW      =    CW

LW             KW

\(\angle {D}=\angle{C}\)