Visual analogy worksheet with geometric shapes and numerical patterns.

Let's solve each analogy step by step. These are visual analogies, where we need to identify the relationship between the first two shapes and apply that same relationship to find the missing shape in the second pair.

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1. D : □ :: C : ?

- D is a letter, and next to it is a square (□).
- Then we have C, and we need to find what corresponds to it.
- This seems like a letter-to-shape mapping.
- But wait — look at the pattern:
- D → square
- C → ?
- Possibly, this is about number of sides or letters with curves vs. straight lines?

But let’s consider:
- D has a curve and a straight line.
- C also has a curve.
- The square has no curves.

Alternatively, maybe this is not about the letters themselves but the shapes associated with them? Wait — perhaps this is misaligned.

Wait — actually, the first row says:
D : □ :: C : ?

But D and C are letters, and then we have shapes. Maybe this is a typo or formatting issue?

Looking more carefully — perhaps this is meant to be a visual pattern, not literal letters.

But the second row starts with a square, then a checkerboard square, then a circle.

So likely, the first row is just labeling the format:
A : B :: C : D — meaning "A is to B as C is to D"

So the first row is just an example of the format:
D : □ :: C : ? — but D and C are letters, and the shapes don't seem to match.

Wait — perhaps it's not D and C as letters, but rather symbols?

Actually, looking closely:

The first row says:
D : □ :: C : ?

But the D and C might be placeholders for shapes? No — they’re letters.

Wait — perhaps this is a typo or misalignment.

But the rest of the rows are all shapes, so maybe the first row is just a title/label.

Let’s skip the first row and go to the actual analogies starting from the second row.

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## Let’s analyze each row one by one.

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Row 2: □ : □ with black squares :: ○ : ?

- First: a white square
- Second: a square divided into four smaller squares, with top-left and bottom-right shaded black — i.e., a checkerboard pattern.
- So: plain white square → checkerboard square
- Then: circle → ?

What’s the transformation?

From plain square to checkerboard: adding a pattern (checkerboard).

But the circle is plain. So what should go after the circle?

Possibly: a circle with a checkerboard pattern inside?

But there's no such thing in the options.

Wait — maybe the pattern is not about coloring, but about division?

Look at the second shape: it's a square divided into 4 equal parts, with alternating black and white.

So: divided into 4 quarters, half shaded.

Now, the third shape is a plain circle.

So if we apply the same transformation: divide the circle into 4 quarters and shade alternately?

That would give a circle with a checkerboard-like pattern.

But since this is a multiple-choice style, and we're to fill in the blank, we need to see what matches.

But the image doesn’t show choices — we must deduce.

Wait — perhaps the pattern is symmetry or shading?

Alternative idea: the second shape is a square with a black-and-white checkerboard, which is symmetric.

But maybe it's about number of regions?

No.

Another idea: the second shape is a square with a pattern, while the first is plain.

So: plain → patterned

Then: plain circle → patterned circle

But what kind of pattern?

Perhaps same as the square’s pattern — but applied to circle.

But circles can’t be divided into 4 squares.

Wait — maybe the checkerboard pattern is just a way of saying “has internal structure”.

But let’s move on and come back.

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Row 3: □ with vertical line :: □ with horizontal line :: ○ with vertical line :: ?

- First: square divided vertically into two rectangles
- Second: square divided horizontally into two rectangles
- Third: circle divided vertically into two semicircles
- Fourth: ?

So: vertical division → horizontal division in the square

So the relationship is: same shape, different orientation of division

So:
- Square: vertical → horizontal
- Circle: vertical → ? → probably horizontal

So answer: circle divided horizontally into two semicircles

So the missing shape is a circle with a horizontal line through the middle.

✔ Answer: circle with horizontal line

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Row 4: △ (outline) :: ▲ (filled triangle) :: ▭ (rectangle with vertical line) :: ?

- First: outline triangle
- Second: solid-filled triangle
- Third: rectangle with a vertical line dividing it into two
- Fourth: ?

So: outline → filled for the triangle

So the transformation is: from outline to filled

Apply to the rectangle: outline rectangle → filled rectangle

But the third shape is already a rectangle with a vertical line — so it's not just outline.

Wait — the third shape is a rectangle split vertically.

So maybe the filling is the key.

But the triangle goes from outline to filled.

So the rectangle should go from outline to filled?

But it’s already split — so maybe the splitting is part of the shape.

Wait — perhaps the third shape is a rectangle with a line, and we need to fill it?

But the analogy is:

△ (outline) → ▲ (filled)
so ▭ (with line) → ?

So the transformation is add fill.

So the missing shape should be the same rectangle with a vertical line, but filled.

So: a filled rectangle with a vertical line.

But the rectangle is split — so filling it would make both halves black.

So: solid black rectangle with a vertical line.

But is that consistent?

Yes — the triangle went from outline to filled, so the rectangle should go from outline to filled.

But the third shape is not outlined — it’s already drawn with a line.

Wait — the third shape is two rectangles side by side, so it's a rectangle with a vertical line, but it’s not shaded.

So perhaps the fourth shape should be the same shape, but filled.

So: filled rectangle with vertical line.

But that’s not a standard shape.

Alternatively, maybe the filling is the key, and the line is secondary.

But the analogy is:

Outline triangle → Filled triangle
Rectangle with line → ?

So yes, same shape, add fill.

So the missing shape is a filled rectangle with a vertical line.

✔ Answer: filled rectangle with vertical line

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Row 5: Pentagon (outline) :: Pentagon (filled) :: Heart (outline) :: ?

- First: outline pentagon
- Second: filled pentagon
- Third: outline heart
- Fourth: ?

So: outline → filled for pentagon

Apply to heart: outline heart → filled heart

So the missing shape is a filled heart.

✔ Answer: filled heart

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Row 6: Circle :: Circle with vertical line :: Triangle :: ?

- First: plain circle
- Second: circle with vertical line
- Third: plain triangle
- Fourth: ?

So: circle → circle with vertical line

Transformation: add a vertical line through the center

Apply to triangle: triangle with vertical line

So: triangle with a vertical line down the middle

This divides the triangle into two parts.

✔ Answer: triangle with vertical line

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Row 7: Dice with 6 dots :: 6 :: Dice with 1 dot :: ?

- First: a die showing 6 dots (standard dice: top row 3 dots, middle row 3 dots)
- Second: the number 6
- Third: a die showing 1 dot (center)
- Fourth: ?

So: die with 6 dots → number 6
→ So: die with 1 dot → number 1

So the missing answer is 1

✔ Answer: 1

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Row 8: Triangle :: 3 :: Square :: ?

- First: triangle
- Second: number 3
- Third: square
- Fourth: ?

So: triangle → 3 — because triangle has 3 sides

So: square → ? — square has 4 sides

So answer: 4

✔ Answer: 4

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Now, going back to Row 2, which we skipped:

Row 2: □ :: □ with checkerboard pattern :: ○ :: ?

- First: plain square
- Second: square with checkerboard pattern (black and white squares)
- Third: plain circle
- Fourth: ?

So: plain square → checkerboard square

What is the transformation?

It's adding a checkerboard pattern — dividing into 4 quadrants and alternating colors.

Now, apply the same to the circle.

But a circle can't be divided into 4 squares — but it can be divided into 4 quadrants.

So: divide the circle into 4 quadrants and color them in checkerboard pattern — i.e., alternate black and white.

So: circle with 4 quadrants, colored in checkerboard

So the missing shape is a circle divided into 4 quarters, with alternating black and white.

This is similar to the square’s pattern.

✔ Answer: circle with checkerboard pattern (quadrants shaded alternately)

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Final Answers:

1. Row 2: Circle with checkerboard pattern (alternating black and white quadrants)
2. Row 3: Circle with horizontal line
3. Row 4: Rectangle with vertical line, filled (solid black)
4. Row 5: Heart filled in (solid black)
5. Row 6: Triangle with vertical line
6. Row 7: 1
7. Row 8: 4

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Summary of Answers (in order):

| Row | Answer |
|-----|--------|
| 2 | Circle with checkerboard pattern (alternating quadrants) |
| 3 | Circle with horizontal line |
| 4 | Rectangle with vertical line, filled |
| 5 | Filled heart |
| 6 | Triangle with vertical line |
| 7 | 1 |
| 8 | 4 |

These are the solutions based on identifying the pattern in each analogy.

Let me know if you'd like a visual representation or explanation of any specific one!