Similar Figures in the Coordinate Plane Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. 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 Yes. All angles are congruent. Yes. All angles are congruent. Yes. All sides are proportional. Yes. All sides are proportional. 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. 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. Skip to navigation page 21 of 21 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

To determine whether triangles ΔFGH and ΔIJK are similar, we generally check two main conditions based on the definitions of transformations:

1. **Angle-Angle (AA) Criterion**: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
2. **Side-Side-Side (SSS) Criterion**: If the lengths of the sides of one triangle are proportional to the lengths of the sides of another triangle, then the triangles are similar.

Without the specific coordinates or the image of the triangles ΔFGH and ΔIJK, we can't draw a decisive conclusion. However, based on the responses provided, we can evaluate potential scenarios:

- If "Yes. All angles are congruent" is true, then ΔFGH∼ΔIJK based on the AA Criterion.
- If "Yes. All sides are proportional" is true, then ΔFGH∼ΔIJK based on the SSS Criterion.

If neither of these statements holds true, then we look at the responses implying that moving point J could potentially make the triangles similar. This suggests that the current coordinates of J do not yield similar triangles.

To summarize:
- If angles are congruent: **ΔFGH∼ΔIJK** (AA)
- If sides are proportional: **ΔFGH∼ΔIJK** (SSS)
- If neither holds, the answer would be based on the current placement of point J.

Based on your question’s reference to point J's potential placements, if adjusting point J could yield similar triangles, the final response regarding the similarity would depend on verifying angle congruence or side proportion based on the specific locations of the triangle's vertices.

If you have the coordinates or aspects of the triangles, I could provide a more precise conclusion on whether they are similar.