ΔXYP ≅ ΔZYP by SSS similarity congruence theorem.
Solution:
Given data:
[tex]\overline{XZ} \perp \overline{WY}[/tex] and [tex]\overline{X Y} \cong \overline{Z Y}[/tex]
To prove [tex]\triangle X Y P \cong \triangle Z Y P[/tex]:
In ΔXYP and ΔZYP,
[tex]\overline {XP} \cong \overline {PZ}[/tex] (given side)
[tex]\overline{X Y} \cong \overline{Z Y}[/tex] (given side)
[tex]\overline{P Y} \cong \overline{P Y}[/tex] (reflexive property)
Therefore ΔXYP ≅ ΔZYP by SSS similarity congruence theorem.
Hence proved.
