Question

Triangle ABC is rotated 95º and then translated 3 units to the left to form triangle DEF. Which statement about the triangles must be true?

a) Triangle DEF will be larger than triangle ABC.
b) Triangle DEF will have an angle that is equal to 95º.
c) Triangle DEF will be congruent to triangle ABC.
d) Triangle DEF will be similar, but not congruent, to triangle ABC.

Answer 1

Triangle DEF will be similar, but not congruent, to triangle ABC. When a triangle is rotated and translated, its size and shape may change, but its angles remain the same.

Step-by-step explanation:

The statement that must be true about the triangles is d) Triangle DEF will be similar, but not congruent, to triangle ABC.

When a triangle is rotated and translated, its size and shape may change, but its angles remain the same. Therefore, Triangle DEF will have an angle equal to 95º (the same as triangle ABC), but it will not be congruent to triangle ABC because the sides may change lengths. However, the triangles will be similar, meaning that their corresponding angles will be equal.

For example, if triangle ABC has side lengths of AB = 4 units, BC = 5 units, and AC = 6 units, triangle DEF may have side lengths of DE = 4.5 units, EF = 5.5 units, and DF = 6.5 units, which are proportional to the corresponding side lengths of triangle ABC.