Step-by-step explanation:
YW bisects the angle XYZ ------(given)
considering Δ XYZ segment XY≅YZ --------given.
∠X≅∠Z angles of opposite equal sides are equal
a triangle having two equal sides is an isosceles triangle. Isosceles triangles have one 90 degrees angles as the total sum of the three angles of a triangle must equal 180 degrees.Therefore ∠Y=90 degrees
but segment YW bisects the angle Y so ∠ZYW= 45 degrees but ∠Z=45 degrees --------(ΔXYZ is a right angled isosceles triangle)
so ∠YWZ=90 degrees as ΔYWZ is also right angled isoseles triangle having two sides equal to 45 and third = 90 degrees.
Hence segmnet YW is perpendicular on segment XZ
