Only the angles of ABCD stay the same in A'B'C'D'! Sliding it doesn't change its shape or size, just its location, so only the angles between lines remain the same. Think of moving a puzzle piece - its angles stay the same, but it's in a new spot. So , Option D) is the only correct statement .
A) Congruence: Translation only shifts the position of a figure, not its size or shape. So, while A'B'C'D' will be identical in every way to ABCD except for its location, they won't be congruent. Imagine sliding a puzzle piece around on a board — it's the same piece, just in a different spot.
B) Dilation: A dilation changes the size of a figure proportionally, but it doesn't change its angles. In this case, A'B'C'D' is the same size and shape as ABCD, so it's not a dilation either. Think of zooming in or out on a photo — the relationships between angles and lines stay the same, only the overall size changes.
C) Size: As mentioned before, translation preserves the size of a figure. So, A'B'C'D' will be the same area and perimeter as ABCD.
D) Angles: This is the only statement that's true! Translation doesn't affect the angles of a figure. The sides and diagonals of ABCD will simply be shifted in parallel, so the angles between them will remain the same in A'B'C'D'.
As you can see, A'B'C'D' is the same shape and size as ABCD, just moved to a different location. The angles between the sides are also the same.
Therefore, the only correct statement is D) The angles of ABCD remain the same in A'B'C'D'.