Question

there are two parts to this question. answer both parts of the question.
part a
triangle abc is rotated counterclockwise by d degrees and then translated by u units to create triangle abc.
is triangle abc congruent to triangle abc? justify your answer.
respond in the space provided.

16b.
part b
triangle abc is reflected over line l and then dilated by a scale factor of r, where r ≠ 1, to create triangle abc.
is triangle abc congruent to triangle abc? justify your answer.
respond in the space provided.

Explanation:

• Part A: Rotation and translation are rigid transformations. Rigid transformations preserve the shape and size of a figure. So, triangle \(ABC\) and triangle \(A'B'C'\) have the same side lengths and angle measures.
• Part B: Reflection is a rigid transformation (preserves shape and size), but dilation with a scale factor \(r

eq1\) changes the size of the figure. If the size of a figure changes, the side - lengths change. Congruent figures must have equal side lengths.

Answer:

• Part A: Yes, triangle \(ABC\) is congruent to triangle \(A'B'C'\). Rotation and translation are rigid transformations that do not change the shape and size of the triangle.
• Part B: No, triangle \(A'B'C'\) is not congruent to triangle \(A''B''C''\). Dilation with a scale factor \(r

eq1\) changes the size of the triangle.