### Given:\(\overline{GJ}\) bisects \(\overline{FH}\), and \(\overline{FH}\) bisects \(\overline{GJ}\).### Prove: \(\triangle FGK \cong \triangle HJK\)### Diagram Explanation:A geometric diagram is shown on the right side which consists of two intersecting lines, labeled \(\overline{FH}\) and \(\overline{GJ}\). The intersection point of these two lines is labeled \(K\).- The endpoints of one line are marked as \(F\) and \(H\).- The endpoints of the other line are labeled \(G\) and \(J\).### Conjecture:Based on the given information, we need to prove that the triangles \( \triangle FGK \) and \( \triangle HJK \) are congruent to each other.### Approach:To prove the congruence of the two triangles:1. Utilize the fact that \( \overline{GJ} \) and \( \overline{FH} \) are bisected at their intersection point \( K \).2. Use geometrical properties and congruence theorems such as Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) to show the required congruence.This problem involves applying the concepts of line segment bisectors and triangle congruence to arrive at the solution.

Name: ### Given:\(\overline{GJ}\) bisects \(\overline{FH}\), and \(\overlin
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: ### Given:\(\overline{GJ}\) bisects \(\overline{FH}\), and \(\overline{FH}\) bisects \(\overline{GJ}\).### Prove: \(\triangle FGK \cong \triangle HJK\)### Diagram Explanation:A geometric diagram is shown on the right side which consists of two inter