Question

drag a figure into each blank space so that the two figures in the row match the description

blue figures: rectangle (8,6), parallelogram (8,6), square (5,5), rhombus (3,3,4,4)

green figure: rectangle (4,3)

rows:

1. not similar but corresponding angles have equal measures

green rectangle (4,3)
drag and drop an item here

1. not similar but side lengths are proportional

green rectangle (4,3)
drag and drop an item here

1. similar

green rectangle (4,3)
drag and drop an item here

Explanation:

Step1: Analyze "Not Similar but Corresponding Angles Have Equal Measures"

Corresponding angles equal means shapes with right angles (rectangles/squares) but not similar (sides not proportional). The first blue figure is a rectangle (6x8), green is 3x4. The blue rectangle (6,8) and green (3,4) have angles 90°, but ratios 6/3=2, 8/4=2? Wait no, wait the green is 3x4, blue rectangle is 6x8: 6/3=2, 8/4=2, that's similar. Wait no, the other blue figures: the parallelogram (not rectangle) vs green? No, the first blue is rectangle (angles 90°), the green is rectangle (3x4). Wait, no, the "Not Similar but Corresponding Angles Equal" should be shapes with equal angles (like rectangles) but sides not proportional. Wait the blue square (5x5) and green (3x4)? No, square has all angles 90°, green is rectangle (90°), but 5/3 ≠5/4. Wait no, the first blue rectangle is 6x8, green is 3x4: 6/3=2, 8/4=2, so similar. Wait maybe the blue rectangle (6x8) and the blue parallelogram? No, parallelogram has angles not 90° unless it's a rectangle. Wait, the "Not Similar but Corresponding Angles Have Equal Measures" – so angles equal (like all 90°) but sides not proportional. Wait the green is 3x4, blue rectangle is 6x8: proportional (2x), so similar. Wait the blue square (5x5) and green (3x4): angles 90°, sides 5/3 ≠5/4, so not similar. But wait the first row: "Not Similar but Corresponding Angles Have Equal Measures" – so we need a shape with equal angles (like rectangle/square) but not similar. The green is 3x4 (rectangle), so we need a blue rectangle or square with angles 90° but sides not proportional to 3x4. The blue rectangle is 6x8 (proportional to 3x4, since 6=2*3, 8=2*4), so similar. The blue square is 5x5: angles 90°, sides 5/3 ≠5/4, so not similar. Wait no, maybe the blue rectangle (6x8) and green (3x4) are similar, so that's not it. Wait the "Not Similar but Corresponding Angles Have Equal Measures" – maybe the blue parallelogram? No, its angles are not 90°. Wait, the first blue figure is a rectangle (angles 90°), green is a rectangle (angles 90°). But 6/3=2, 8/4=2, so similar. So maybe the blue square (5x5) and green (3x4): angles 90°, sides not proportional. But the green is 3x4, blue square is 5x5. So that's not similar. But the problem says "drag a figure" – maybe the first blue rectangle (6x8) and green (3x4) are similar, so that's the "Similar" row. Wait let's re-express:

- Similar: shapes with proportional sides and equal angles. So green 3x4, blue rectangle 6x8: 6/3=2, 8/4=2, so similar. So "Similar" row: drag the blue rectangle (6x8) to the third row.

- "Not Similar but Corresponding Angles Have Equal Measures": angles equal (90°) but sides not proportional. Green is 3x4 (rectangle), so blue square (5x5): angles 90°, sides 5/3 ≠5/4, so not similar. So drag blue square to first row.

- "Not Similar but Side Lengths Are Proportional": sides proportional but angles not equal. So sides proportional (like 3,3,4,4 and green 3,4? Wait the blue rhombus (3,3,4,4) and green 3,4: sides 3/3=1, 4/4=1, but angles: rhombus has angles not 90°, green is rectangle (90°), so sides proportional (3/3=1, 4/4=1) but angles not equal, so not similar. So drag blue rhombus to second row.

Wait let's formalize:

1. Similar: Sides proportional, angles equal. Green 3x4, blue rectangle 6x8: 6/3=2, 8/4=2, so similar. So third row (Similar) gets blue rectangle (6x8).

2. Not Similar but Corresponding Angles Equal: Angles equal (90°) but sides not proportional. Green 3x4, blue square 5x5: angles 90°, 5/3 ≠5/4, so not similar. So first row gets blue square (5x5).

3. Not Similar but Side Lengths Proportional: Sides proportional but angles not equal. Green 3x4, blue rhombus (3,3,4,4): sides 3/3=1, 4/4=1 (proportional), but rhombus angles not 90°, green is rectangle (90°), so not similar. So second row gets blue rhombus (3,3,4,4).

Wait let's check each:

- Similar: The blue rectangle (6,8) and green (3,4) have ratio 2, so similar. Correct.

- Not Similar but Corresponding Angles Equal: Blue square (5,5) and green (3,4). Both have 90° angles, but 5/3 ≠5/4, so not similar. Correct.

- Not Similar but Side Lengths Proportional: Blue rhombus (3,3,4,4) and green (3,4). Sides: 3/3=1, 4/4=1 (proportional), but rhombus angles are not 90° (it's a diamond with sides 3,3,4,4 – actually a rhombus? Wait no, a rhombus has all sides equal, but this has two sides 3 and two 4, so it's a parallelogram with sides 3,4,3,4. So it's a parallelogram, green is a rectangle (a type of parallelogram with 90° angles). So sides are proportional (3/3=1, 4/4=1), but angles: parallelogram has angles not 90° (unless it's a rectangle), so angles not equal, but sides proportional. So that's "Not Similar but Side Lengths Are Proportional".

So:

- "Not Similar but Corresponding Angles Have Equal Measures": Drag the blue square (5x5) (since it's a square, angles 90°, sides not proportional to 3x4).

- "Not Similar but Side Lengths Are Proportional": Drag the blue rhombus (3,3,4,4) (sides proportional to 3,4,3,4, angles not 90°).

- "Similar": Drag the blue rectangle (6x8) (sides proportional to 3x4, angles 90°).

Step2: Assign to Rows

1. "Not Similar but Corresponding Angles Have Equal Measures": Blue square (5x5).

2. "Not Similar but Side Lengths Are Proportional": Blue rhombus (3,3,4,4).

3. "Similar": Blue rectangle (6x8).

Answer:

• Not Similar but Corresponding Angles Have Equal Measures: Drag the blue square (5 by 5).
• Not Similar but Side Lengths Are Proportional: Drag the blue rhombus (3, 3, 4, 4).
• Similar: Drag the blue rectangle (6 by 8).