Question

If 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

Answer 1

A translation that maps ∠I onto ∠K ensures that the angles are congruent due to the properties of translations in geometry, hence ∠H ≅ ∠J is the true statement.

Step-by-step explanation:

If a translation maps ∠I onto ∠K, it means that the two angles are congruent, so ∠H ≅ ∠J by corresponding parts of congruent triangles. This is because translations in geometry move every point a constant distance in a specified direction, leading to congruent figures which preserve angles and side lengths.

The question does not provide information to support that segment HI is twice the measure of segment JK, segment GH is twice the measure of segment GJ, or to conclude that triangles ΔGHI and ΔGJK are not similar.

The information given is insufficient to establish these statements, we only know that angles are preserved under translation.

Therefore, the correct statement regarding the translation of ∠I to ∠K is that ∠H ≅ ∠J.