Question

If a translation maps ∠i onto ∠k, which of the following statements is true?

Option 1: Segment hi = segment jk
Option 2: Δghi ~ Δgjk
Option 3: Segment gh = segment gj
Option 4: ∠g ≅ ∠k

Answer 1

A translation maps angles, not line segments or entire triangles. If a translation maps ∠i onto ∠k, the correct statement would be ∠g ≅ ∠k.

Step-by-step explanation:

If a translation maps ∠i onto ∠k, it means that the two angles are congruent or equal in measure. In other words, ∠i ≅ ∠k. With this understanding, let's evaluate the given options:

1. Option 1: Segment hi = segment jk – This statement is not necessarily true because a translation only maps angles, not line segments.
2. Option 2: Δghi ~ Δgjk – This statement is also not necessarily true because a translation only maps individual angles, not entire triangles.
3. Option 3: Segment gh = segment gj – This statement is not necessarily true because a translation only maps angles, not line segments.
4. Option 4: ∠g ≅ ∠k – This statement is true because a translation maps ∠i onto ∠k, which means they are congruent or equal in measure.

Therefore, the correct answer is

Option 4: ∠g ≅ ∠k

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