Use the image to answer the question.

Question

Triangle F G H is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle J K I is drawn with a dotted line and is located in quadrant 4.

Assess two figures using the definitions of transformations to determine whether the figures are similar. Is ΔFGH∼ΔIJK
, and for what reason?

(1 point)
Responses

No. If point J
was at (−6,6)
, the triangles would be similar.
No. If point upper J was at left parenthesis negative 4 comma 5 right parenthesis , the triangles would be similar.

Yes. All angles are congruent.
Yes. All angles are congruent.

No. If point J
was at (6,−6)
, the triangles would be similar.
No. If point upper J was at left parenthesis 4 comma negative 5 right parenthesis , the triangles would be similar.

Yes. All sides are proportional.

Answer 1

In order to determine if triangles \( \Delta FGH \) and \( \Delta IJK \) are similar, we need to assess their angles and side lengths.

1. Angle Congruence: For two triangles to be similar, one criterion is that all corresponding angles must be equal (congruent). If you find that all angles in triangle \( \Delta FGH \) are congruent to the corresponding angles in triangle \( \Delta IJK \), that establishes similarity.

2. Proportional Side Lengths: Another criterion is that all corresponding sides must be in proportion. If the ratios of the lengths of corresponding sides are equal, then the triangles are similar.

Without the specific measurements or angles given in the image, we cannot definitively conclude the relationship between the triangles. However, based on the options provided:

The most fitting responses appear to be related to angle congruence or side proportionality.

Given these observations, if the triangles indeed have all angles congruent or all sides proportional, the correct response would reflect that.

Based on your options, if it is established that their angles are congruent, then the correct response would be:

"Yes. All angles are congruent."

If they have proportional sides instead, the response would be:

"Yes. All sides are proportional."

However, without the image or specific measurements, I can't definitively choose between those two options without more context.