\(WZ\) and \(XY\) are equal perpendiculars to a line segment \(WX\). Show that \(YZ\) bisects \(WX\).
Proof:
In \(ΔWOZ\) and \(ΔXOY\), we have:
Here, \(∠ WOZ= ∠ \) [Vertically opposite angles] ---- (i)
\(∠ OWZ = ∠OX Y\) [perpendiculars] ----- (ii)
\(WZ= XY \) [Given] ----- (iii)
Thus, by congruence rule\(ΔWOZ ≅ ΔXOY\)
So, \(WO = XO\) [By CPCT]
Hence, \(YZ\) bisects \(WX\) at \(O\).
Hence, we proved.