The images show various quadrilaterals, and you're asked to identify which pairs of shapes are similar. To determine similarity, we need to check if the shapes have proportional sides and the same angle measures.

Image 1:

• Top-left quadrilateral (D, E, G, F) has four equal sides (48 yd) and right angles, meaning it's a square.
• Top-right quadrilateral (T, U, W, V) has sides 42 yd and 48 yd, with right angles, so it's a rectangle.
• Bottom-left quadrilateral (C, D, E, F) has sides 22, 26, 37, and 26 mm, and right angles. This is a rectangle.
• Bottom-right quadrilateral (L, K, I, J) has sides 20, 25, 37, and 20 mm, and right angles. This is a rectangle.

Similarity Check:

• Top-left and top-right: These are not similar because the side lengths do not have proportional relationships (48 yd vs. 42 yd, 48 yd vs. 42 yd).
• Bottom-left and bottom-right: These two rectangles are similar because they both have right angles, and the corresponding side lengths are proportional. Their ratios of side lengths match (22:20 and 26:25).

Image 2:

• Top-left quadrilateral (J, K, L, M) is a rectangle with sides 25 mi, 40 mi.
• Top-right quadrilateral (T, U, R, S) is a rectangle with sides 30 mi and 48 mi.
• Bottom-left quadrilateral (M, P, N, O) is a rectangle with sides 23 km.
• Bottom-right quadrilateral (V, W, X, Y) is a square with all sides equal (29 km).

Similarity Check:

• Top-left and top-right: These two rectangles are not similar because the side lengths are not proportional (25:30 and 40:48).
• Bottom-left and bottom-right: These are not similar because one is a square and the other is a rectangle.

Conclusion:

• The bottom-left (Image 1) and bottom-right (Image 1) rectangles are similar.
• The bottom-left (Image 2) and bottom-right (Image 2) figures are not similar.

If you have more questions or would like further explanations, feel free to ask! Here are 5 follow-up questions you might find interesting:

1. How do you calculate the similarity of triangles?
2. What are the properties of similar quadrilaterals?
3. What does proportionality mean in geometry?
4. Can two shapes have the same perimeter but not be similar?
5. How can you identify similar polygons in real-life scenarios?

Tip: To check for similarity in polygons, always compare the ratios of corresponding side lengths and make sure the angles match.