Question

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

Answer 1

Given,

angle 5 = angle 6

JG is thealtitude to segment FH.

In triangle FJG and triangle FHG,

`\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}`

Then,

`FJ=HJ(By\text{ CPCT)}`

As, the two sides of the triangle is equal. So, triangle FJH is isosceles triangle.

Hence, FJH is isosceles triangle.