In ΔXYZ, ∠YXZ = 90 degree. P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm, then what will be value of PZ?

10 cm

We have,

∠YXZ = 90 degree

XP = YP = 10 cm

In ΔXYZ,

∠YXZ = 90 degree

If ∠Y = θ , then

=∠Z = 90 - θ 

In ΔXPY,

=∠YPX = 90°      [Given]

=∠Y = ∠YXP = θ      [XP = PY]

In ΔXPZ,

= ∠XPZ = 90°      [Given]

= ∠PXZ = 90 - θ    

⇒ ∠Z = 90 - θ 

ΔXPZ is isosceles triangle. Then, = XP = PZ = 10 cm