f a translation maps ∠I onto ∠K, which of the following statements is true? Triangles HGI and JGK; point H is between points J and G on segment JG, and point I is between points G and K on segment GK. segment HI is twice the measure of segment JK. segment GH is twice the measure of segment GJ. Triangles ΔGHI and ΔGJK are not similar. ∠H ≅ ∠J

The correct option is;

∠H ≅ ∠J

Step-by-step explanation:

Given that a translation maps ∠I onto ∠K, therefore;

in triangles GHI and GJK we have;

∠I ≅ ∠K; Given

∠G = ∠G; Reflexive property

Therefore, ∠H + ∠I + ∠G = 180° (Sum of interior angles in a triangle)

Similarly,  ∠J + ∠K + ∠G = 180° (Sum of interior angles in a triangle)

Which gives;

∠H  = 180° - (∠I + ∠G) = 180° - (∠K + ∠G) = ∠J

Therefore, angle K and angle H are congruent which can be expressed as follows;

∠H ≅ ∠J.

thats not a system of equations, that is a solution