Question

The vertices of ΔABC are A (1, 2), B (3, 9), and C (1, 5). The vertices of ΔDEF are D (5, 2), E (1, -9), and F (13, 0).

Which conclusion is true about the triangles?
A. The ratio of their corresponding sides is 1:3.
B. They are congruent by the definition of congruence in terms of rigid motions.
C. The ratio of their corresponding angles is 1:3.
D. They are similar by the definition of similarity in terms of a dilation.

Answer 1

The given triangles ΔABC and ΔDEF are similar by the definition of similarity in terms of a dilation.

Step-by-step explanation:

The given triangles are ΔABC and ΔDEF. To determine the relationship between the two triangles, we can compare their corresponding sides and angles.

By calculating the distance between the vertices, we find that AB = 8 and DE = 8. Therefore, the ratio of AB to DE is 1:1, which means the corresponding sides are congruent. Thus, we can conclude that the triangles are similar by the definition of similarity in terms of a dilation.