Use the image to answer the question.

Question

An illustration shows a 12 by 9 grid that has a parallelogram, a square, and a rotated square on it. Figure 1 is a parallelogram. The top side occupies 3 units along top of the 2nd row from the start of 5th to the end of 7th columns. The bottom side occupies 3 units along the base of the 3rd row, from the start of the 3rd to the end of the 5th columns. Figure 2, a square, extends from the start of the 3rd to the end of the 4th rows, and the start of the 9th to the end of the 10th rows. Figure 3 is a square rotated 45 degrees. It has the top vertex at the top of the 5th row, between the 5th and 6th columns. The right vertex is between the 6th and 7th rows at the end of the 7th column. The bottom vertex is at the end of the 8th row, between the 5th and 6th columns. The left vertex is between the 6th and 7th rows at the start of the 4th column. All the vertices are at the intersection of the grid lines.

Which of the figures in the image are similar? Enter the smaller figure number first followed by the larger figure number.(1 point)
Figure
and Figure

Answer 1

To determine which of the figures are similar, we need to analyze their shapes and properties.

1. Figure 1 (Parallelogram): This shape has opposite sides that are equal in length and parallel, but it is not a rectangle or square.

2. Figure 2 (Square): This shape has all sides equal and all angles at 90 degrees.

3. Figure 3 (Rotated Square): While this shape looks like a diamond due to being rotated, it still has all sides equal and all angles are at 90 degrees because a rotated square is still a square.

Since Figure 2 is a square and Figure 3 is a square (albeit rotated), they are similar because they have the same shape even though one is rotated. Figure 1 (the parallelogram) cannot be similar to the squares since its angles and side ratios differ.

Therefore, the figures that are similar are: Figure 2 and Figure 3.