Question

Triangle ABC undergoes a series of transformations to make triangle A'B'C'.

Which statements are true?
A.A rotation of triangle ABC by 60°, followed by a reflection over the line x = 3, will result in triangle ABC being congruent to triangle A'B'C'.
B.A reflection of triangle ABC over the y -axis, followed by a dilation by a factor of 2, will result in triangle ABC being congruent to triangle A'B'C'.
C.A rotation of triangle ABC by 180°, followed by a translation of 3 units horizontally, will result in triangle ABC not being congruent to triangle A'B'C'.
D.A dilation of triangle ABC by a factor of 0.5, followed by a translation of 5 units vertically, will result in triangle ABC not being congruent to triangle A'B'C'.
E.A translation of triangle ABC of 3 units horizontally and 2 units vertically, followed by a reflection over the x-axis, will result in triangle ABC being congruent to triangle A'B'C'.

Answer 1

Statement E is the only true statement. A combination of translation, reflection, and dilation can result in congruent triangles.

Step-by-step explanation:

Statement A: A rotation of triangle ABC by 60°, followed by a reflection over the line x = 3, will result in triangle ABC being congruent to triangle A'B'C'.

Statement B: A reflection of triangle ABC over the y-axis, followed by a dilation by a factor of 2, will result in triangle ABC being congruent to triangle A'B'C'.

Statement C: A rotation of triangle ABC by 180°, followed by a translation of 3 units horizontally, will result in triangle ABC not being congruent to triangle A'B'C'.

Statement D: A dilation of triangle ABC by a factor of 0.5, followed by a translation of 5 units vertically, will result in triangle ABC not being congruent to triangle A'B'C'.

Statement E: A translation of triangle ABC of 3 units horizontally and 2 units vertically, followed by a reflection over the x-axis, will result in triangle ABC being congruent to triangle A'B'C'.

Only Statement E is true. A combination of translation, reflection, and dilation can result in congruent triangles.