Determine whether the triangles are similar. If so, what is the similarity statement and the postulate or theorem used.
a. ΔDGH ~ ΔDFE, SSS ~
b. ΔDGH ~ ΔDFE, SAS ~
c. ΔDGH ~ ΔFEG, SAS ~
d. The triangles are not similar
Image:
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ΔABC ~
To determine whether the triangles are similar and to find the similarity statement and the postulate or theorem used for each case, we look for corresponding sides or angles that have a proportional relationship.
a. ΔDGH ~ ΔDFE, using the SSS (Side-Side-Side) similarity postulate. This postulate states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
b. ΔDGH ~ ΔDFE, using the SAS (Side-Angle-Side) similarity postulate. This postulate states that if an angle of one triangle is congruent to an angle of another triangle, and the corresponding sides including these angles are proportional, then the triangles are similar.
c. ΔDGH ~ ΔFEG, using the SAS (Side-Angle-Side) similarity postulate. This is the same postulate as in part b, stating that if an angle of one triangle is congruent to an angle of another triangle, and the corresponding sides including these angles are proportional, then the triangles are similar.
d. The triangles are not similar if none of the above conditions are met. In the given image, we cannot conclude the similarity of ΔABC to any other triangles as we do not have enough information.
Please note that due to the inability to display the image and refer to specific sides and angles, the above statements are based on general similarity postulates and the given options.