To determine whether triangles ΔFGH and ΔIJK are similar, we typically check two main criteria: if the corresponding angles are congruent and if the corresponding sides are in proportion.
Since I do not have access to the image, I will guide you on how to perform the assessment:
-
Check for Congruent Angles: If all corresponding angles in ΔFGH and ΔIJK are congruent, then the triangles are similar by the Angle-Angle (AA) postulate.
-
Check for Proportional Sides: If the lengths of corresponding sides of the triangles are proportional, then the triangles are similar by the Side-Side-Side (SSS) similarity theorem.
-
Coordinates of Points: If you have the coordinates of the vertices for both triangles, you can calculate the side lengths using the distance formula. You would also be able to verify the angles, although that usually requires geometric construction or other calculations.
Now, looking at the possible responses:
- If you conclude that all angles are congruent, then you would respond with "Yes. All angles are congruent."
- If you conclude that all sides are proportional, then you would respond with "Yes. All sides are proportional."
- If neither condition for similarity is met, you can consider the options about the specific placement of point J.
To answer the question based on the conditions of similarity (regardless of the specific details of the image you may have), you will ultimately need to confirm either angle congruence or side proportionality to definitively state whether the triangles are similar. Consider these criteria carefully based on the given options!
1 answer