Geometry question: Given <5 = <6, Segment JG is the altitude to segment FH, prove triangle FJH is isosceles.

Given,
angle 5 = angle 6
JG is thealtitude to segment FH.
In triangle FJG and triangle FHG,
[tex]\begin{gathered} \angle5=\angle6(given) \\ JG=JG\text{ (common side)} \\ \angle JGH=\angle JGF\text{ (rightangle)} \\ \Delta FJG\cong\Delta FHG\text{ (By angle - side - angle congruence theorem)} \end{gathered}[/tex]Then,
[tex]FJ=HJ(By\text{ CPCT)}[/tex]As, the two sides of the triangle is equal. So, triangle FJH is isosceles triangle.
Hence, FJH is isosceles triangle.