Similar Figures Practice

Question

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Question
Use the image to answer the 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
Remaining Attempts : 3
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Answer 1

To determine which figures are similar, we need to examine their properties, particularly focusing on their angles and side ratios.

1. Figure 1 (Parallelogram): Parallelograms have opposite sides that are equal in length and opposite angles that are equal as well. However, without additional details about the angles, we can’t conclude if it is similar to either of the squares.

2. Figure 2 (Square): By definition, a square has all sides equal and all angles equal to 90 degrees.

3. Figure 3 (Rotated Square): A square rotated does not change its inherent properties—it still has all sides equal and all angles equal to 90 degrees.

Since Figure 2 (the square) and Figure 3 (the rotated square) have the same shape properties (equal sides and angles), they are similar to each other.

Therefore, the answer is: Figure 2 and Figure 3.