Final answer:
To prove that GI is perpendicular to HJ, we must use congruent angles and geometric properties to demonstrate that the angles formed by GI and HJ are right angles. Without additional information or a diagram, the proof cannot be constructed.
Step-by-step explanation:
To demonstrate that GI is perpendicular to HJ, based on the assertion that angle HKI is congruent to angle GKH, we need to examine the relationship between the angles and sides of the relevant geometric figures involved. Unfortunately, without a complementary figure or additional information about the points and lines in question, deriving the proof is not possible.Since angle hki is a right angle, gkj is perpendicular to hi (line segments perpendicular to the same line are parallel to each other).
However, if we are to deduce the perpendicularity based on congruent angles, we must show that the angles formed by the intersection of GI and HJ are right angles (90 degrees). Congruent angles and the properties of geometric figures such as triangles and the Pythagorean theorem could be employed to demonstrate the perpendicular relationship.