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Figure Analogy - Beginner Level: visual analogies BEGINNER

This foundation builder 🌟 worksheet contains 20 beginner-level figure analogy problems. Worksheet 1 of 30 focuses on visual analogies. Practice visual analogies, shape relationships, image analogies with our step-by-step solutions. Difficulty: foundational concepts and basic patterns. Recommended for entry-level learners.

📝 Worksheet 1 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Figure Analogy
Worksheet 1 of 30 (3% complete)

Question 1

Figure Analogy: A : B :: C : ? Rule: If a figure has more than 4 sides, add a central dot. Otherwise, keep unchanged. Apply to C.
Step-by-Step Solution:

STEP 1: Analyze Figure A Properties
- Shape: Pentagon (5-sided polygon)
- Sides count: 5 > 4 ✓
- Internal elements: None initially

STEP 2: Analyze Figure B (Result)
- Shape: Pentagon (5-sided polygon - same as A)
- Internal elements: One central dot added
- Transformation applied: Dot added (condition met)

STEP 3: Extract Transformation Rule
- Condition: Count number of sides
- Decision point: Compare to 4
- If sides > 4: Add central dot
- If sides ≤ 4: No change

STEP 4: Analyze Figure C Properties
- Shape: Rectangle (4-sided polygon)
- Sides count: 4 = 4 (NOT greater than 4)
- Current internal elements: None

STEP 5: Apply Conditional Rule to C
- Rectangle has 4 sides
- Is 4 > 4? NO
- Condition NOT met
- Action: NO transformation (keep unchanged)

Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
conditional, rule-based, logical-condition

Question 2

Figure Analogy: A : B :: C : ? Figure A has 1 dot(s). Figure B has 3 dot(s) (2 more). Apply the same transformation to Figure C.
Step-by-Step Solution:

STEP 1: Identify Numerical Pattern
- A: 1 dot(s)
- B: 3 dot(s)
- Change: +2 dot(s) added

STEP 2: Apply to Figure C
- C: 1 dot(s) (different container)
- Add 2 more dot(s)
- Result: 3 dots total

Answer: Square with 3 dots (2 more than original)
quantitative, progression, element-addition

Question 3

Figure Analogy: A : B :: C : ? A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation - Rotation
- Figure A: Diamond (square rotated 45°)
- Figure B: Diamond rotated further (additional 45° clockwise)
- First transformation: 45° clockwise rotation

STEP 2: Identify Second Transformation - Scaling
- Measure A diagonal span: Approximately 36 units
- Measure B diagonal span: Approximately 48 units
- Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3)
- Second transformation: 1.3× scaling (30% enlargement)

STEP 3: Identify Third Transformation - Color Inversion
- Figure A fill: White (light), dot: Black (dark)
- Figure B fill: Black (dark), dot: White (light)
- Third transformation: Complete color/shading inversion

STEP 4: Analyze Figure C
- Shape: Rectangle (horizontal orientation)
- Size: Standard (40×34 units)
- Colors: White background, black internal lines
- Internal elements: 2 perpendicular lines (cross pattern)

STEP 5: Apply Transformations in Sequence
- Rotate 45° clockwise → Rectangle becomes tilted (diamond-like)
- Scale 1.3× → All dimensions multiplied by 1.3
- Invert colors → Black background, white lines

Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
multi-step, complex, three-transformations

Question 4

Figure Analogy: A : B :: C : ? Figure A is enlarged by 3× to become Figure B. What should Figure '?' look like when the same scaling is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Scaling Factor
- Figure A square: 25 units
- Figure B square: 75 units
- Scaling factor = 75/25 = 3

STEP 2: Apply to Figure C
- Figure C: Circle
- Apply scaling factor 3
- New dimensions = original × 3

STEP 3: Verify
- Shape type preserved ✓
- Proportions preserved ✓
- Only size changed ✓

Answer: Circle enlarged by 3×
scaling, size-change, proportional

Question 5

Figure Analogy: A : B :: C : ? In A→B, all shaded regions become unshaded and vice versa (color inversion). Apply the same inversion to Figure C.
Step-by-Step Solution:

STEP 1: Identify Transformation
- A: Light background, dark internal elements
- B: Dark background, light internal elements
- Rule: Complete color/shading inversion

STEP 2: Apply to Figure C
- C: Light background, dark internal elements
- After inversion: Dark background, light internal elements
- All positions and shapes preserved

Answer: Square with inverted shading
inversion, shading, color-swap

Question 6

Figure Analogy: A : B :: C : ? Figure A undergoes two transformations to become B: rotated 90° anticlockwise AND enlarged by 1.5x. Apply both to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation (Rotation)
- Figure A orientation: Triangle pointing right
- Figure B orientation: Triangle pointing upward
- First transformation: 90° anticlockwise rotation

STEP 2: Identify Second Transformation (Scaling)
- Measure A dimensions: Small triangle (base ≈ 20 units)
- Measure B dimensions: Larger triangle (base ≈ 30 units)
- Second transformation: 1.5× scaling (enlargement by 50%)

STEP 3: Determine Transformation Sequence
- Method 1: Rotate first, then scale
- Method 2: Scale first, then rotate
- Result: Same final figure (transformations commute)
- Standard approach: Rotate, then scale

STEP 4: Apply Rotation to C (90° anticlockwise)
- Original C: Vertical rectangle (height > width)
- After rotation: Horizontal rectangle (width > height)
- Internal dot: Rotates with figure to new position

STEP 5: Apply Scaling to Rotated C (1.5×)
- Current dimensions: Already rotated rectangle
- Apply 1.5× to both length and width
- Internal dot: Maintains relative position, scales proportionally

STEP 6: Verify Combined Transformation
- Original: Vertical rectangle, small size, dot at top
- After rotation: Horizontal rectangle, small size, dot on left
- After scaling: Horizontal rectangle, 1.5× larger, dot on left (scaled position)

Answer: Rectangle in horizontal orientation (rotated 90° anticlockwise), dimensions increased by 1.5×, with dot repositioned according to both transformations
multi-step, rotation, scaling, combined-transformation

Question 7

Figure Analogy: A : B :: C : ? In A→B, all shaded regions become unshaded and vice versa (color inversion). Apply the same inversion to Figure C.
Step-by-Step Solution:

STEP 1: Identify Transformation
- A: Light background, dark internal elements
- B: Dark background, light internal elements
- Rule: Complete color/shading inversion

STEP 2: Apply to Figure C
- C: Light background, dark internal elements
- After inversion: Dark background, light internal elements
- All positions and shapes preserved

Answer: Square with inverted shading
inversion, shading, color-swap

Question 8

Figure Analogy: A : B :: C : ? In A→B, all shaded regions become unshaded and vice versa (color inversion). Apply the same inversion to Figure C.
Step-by-Step Solution:

STEP 1: Identify Transformation
- A: Light background, dark internal elements
- B: Dark background, light internal elements
- Rule: Complete color/shading inversion

STEP 2: Apply to Figure C
- C: Light background, dark internal elements
- After inversion: Dark background, light internal elements
- All positions and shapes preserved

Answer: Square with inverted shading
inversion, shading, color-swap

Question 9

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Triangle with inscribed triangle (inner becomes triangle)
shape-change, morphing, property-matching

Question 10

Figure Analogy: A : B :: C : ? A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation - Rotation
- Figure A: Diamond (square rotated 45°)
- Figure B: Diamond rotated further (additional 45° clockwise)
- First transformation: 45° clockwise rotation

STEP 2: Identify Second Transformation - Scaling
- Measure A diagonal span: Approximately 36 units
- Measure B diagonal span: Approximately 48 units
- Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3)
- Second transformation: 1.3× scaling (30% enlargement)

STEP 3: Identify Third Transformation - Color Inversion
- Figure A fill: White (light), dot: Black (dark)
- Figure B fill: Black (dark), dot: White (light)
- Third transformation: Complete color/shading inversion

STEP 4: Analyze Figure C
- Shape: Rectangle (horizontal orientation)
- Size: Standard (40×34 units)
- Colors: White background, black internal lines
- Internal elements: 2 perpendicular lines (cross pattern)

STEP 5: Apply Transformations in Sequence
- Rotate 45° clockwise → Rectangle becomes tilted (diamond-like)
- Scale 1.3× → All dimensions multiplied by 1.3
- Invert colors → Black background, white lines

Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
multi-step, complex, three-transformations

Question 11

Figure Analogy: A : B :: C : ? Figure A is enlarged by 3× to become Figure B. What should Figure '?' look like when the same scaling is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Scaling Factor
- Figure A circle: 20 units
- Figure B circle: 60 units
- Scaling factor = 60/20 = 3

STEP 2: Apply to Figure C
- Figure C: Square
- Apply scaling factor 3
- New dimensions = original × 3

STEP 3: Verify
- Shape type preserved ✓
- Proportions preserved ✓
- Only size changed ✓

Answer: Square enlarged by 3×
scaling, size-change, proportional

Question 12

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid
set-operations, union, geometric-logic

Question 13

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid
set-operations, union, geometric-logic

Question 14

Figure Analogy: A : B :: C : ? Rule: If a figure has more than 4 sides, add a central dot. Otherwise, keep unchanged. Apply to C.
Step-by-Step Solution:

STEP 1: Analyze Figure A Properties
- Shape: Pentagon (5-sided polygon)
- Sides count: 5 > 4 ✓
- Internal elements: None initially

STEP 2: Analyze Figure B (Result)
- Shape: Pentagon (5-sided polygon - same as A)
- Internal elements: One central dot added
- Transformation applied: Dot added (condition met)

STEP 3: Extract Transformation Rule
- Condition: Count number of sides
- Decision point: Compare to 4
- If sides > 4: Add central dot
- If sides ≤ 4: No change

STEP 4: Analyze Figure C Properties
- Shape: Rectangle (4-sided polygon)
- Sides count: 4 = 4 (NOT greater than 4)
- Current internal elements: None

STEP 5: Apply Conditional Rule to C
- Rectangle has 4 sides
- Is 4 > 4? NO
- Condition NOT met
- Action: NO transformation (keep unchanged)

Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
conditional, rule-based, logical-condition

Question 15

Figure Analogy: A : B :: C : ? Figure A is rotated 90° anticlockwise to become Figure B. What should Figure '?' look like when the same rotation is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Transformation
- Figure A: Triangle in original orientation
- Figure B: Same triangle rotated 90° anticlockwise
- Transformation: 90° anticlockwise rotation

STEP 2: Apply to Figure C
- Figure C: Rectangle (horizontal orientation)
- After 90° anticlockwise rotation: Rectangle becomes vertical
- The shape remains a rectangle, only orientation changes

STEP 3: Verify
- Shape preserved ✓
- Size preserved ✓
- Only orientation changed by 90° anticlockwise ✓

Answer: Rectangle rotated 90° anticlockwise (becomes vertical)
rotation, orientation, basic-transformation

Question 16

Figure Analogy: A : B :: C : ? Pattern: The number of sides of the outer shape becomes the number of sides of the inner shape, and the inner shape's side count determines the new outer shape's side count through a progressive relationship (Circle→Hexagon→Octagon). Apply to C.
Step-by-Step Solution:

STEP 1: Analyze Figure A
- Outer shape: Circle (can be considered as infinite or 0 sides)
- Inner shape: Diamond (4 sides)

STEP 2: Analyze Figure B
- Outer shape: Hexagon (6 sides)
- Inner shape: Circle (infinite sides)

STEP 3: Identify the Pattern
Looking at the progression:
- A: Outer Circle (∞), Inner Diamond (4)
- B: Outer Hexagon (6), Inner Circle (∞)

The transformation swaps and transforms side counts:
- The inner shape's side count (4) becomes part of the new outer shape
- The pattern shows: 4 → 6 → 8 (increasing by 2 each time)
- Circle (∞) acts as a placeholder that transforms to the next polygon in sequence

STEP 4: Analyze Figure C
- Outer shape: Hexagon (6 sides)
- Inner shape: Diamond (4 sides)

STEP 5: Apply Pattern to C
Following the established pattern:
- The inner diamond has 4 sides → following the 4→6→8 progression, this contributes to the new outer shape
- The outer hexagon has 6 sides → this becomes the new inner shape's side count
- Therefore: New outer = Octagon (8 sides), New inner = Hexagon (6 sides)

STEP 6: Verify Pattern Consistency
- A: Circle (∞) + Diamond (4) → B: Hexagon (6) + Circle (∞)
- C: Hexagon (6) + Diamond (4) → ?: Octagon (8) + Hexagon (6)
- The pattern shows that the inner shape's side count determines the progression of the outer shape

Answer: Octagon (8 sides) with hexagon (6 sides) inside

Key Insight: This problem tests recognition of progressive relationships where shapes evolve based on their side counts, with circle acting as a special case that transforms to the next polygon in the sequence.
abstract, complex-pattern, advanced-reasoning

Question 17

Figure Analogy: A : B :: C : ? Figure A has 1 dot. Figure B has 3 dots (2 more). Apply the same transformation to Figure C.
Step-by-Step Solution:

STEP 1: Count Elements in A and B
- Figure A: Triangle + 1 dot
- Figure B: Triangle + 3 dots
- Change: +2 dots added

STEP 2: Apply to Figure C
- Figure C: Different container + 1 dot
- Add 2 more dots
- Result: Container + 3 dots total

Answer: Circle with 3 dots (1 original + 2 added)
element-count, addition, quantitative

Question 18

Figure Analogy: A : B :: C : ? Figure A is enlarged by 2× to become Figure B. What should Figure '?' look like when the same scaling is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Scaling Factor
- Figure A square: 25 units
- Figure B square: 50 units
- Scaling factor = 50/25 = 2

STEP 2: Apply to Figure C
- Figure C: Circle
- Apply scaling factor 2
- New dimensions = original × 2

STEP 3: Verify
- Shape type preserved ✓
- Proportions preserved ✓
- Only size changed ✓

Answer: Circle enlarged by 2×
scaling, size-change, proportional

Question 19

Figure Analogy: A : B :: C : ? Rule: If a figure has more than 4 sides, add a central dot. Otherwise, keep unchanged. Apply to C.
Step-by-Step Solution:

STEP 1: Analyze Figure A Properties
- Shape: Pentagon (5-sided polygon)
- Sides count: 5 > 4 ✓
- Internal elements: None initially

STEP 2: Analyze Figure B (Result)
- Shape: Pentagon (5-sided polygon - same as A)
- Internal elements: One central dot added
- Transformation applied: Dot added (condition met)

STEP 3: Extract Transformation Rule
- Condition: Count number of sides
- Decision point: Compare to 4
- If sides > 4: Add central dot
- If sides ≤ 4: No change

STEP 4: Analyze Figure C Properties
- Shape: Rectangle (4-sided polygon)
- Sides count: 4 = 4 (NOT greater than 4)
- Current internal elements: None

STEP 5: Apply Conditional Rule to C
- Rectangle has 4 sides
- Is 4 > 4? NO
- Condition NOT met
- Action: NO transformation (keep unchanged)

Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
conditional, rule-based, logical-condition

Question 20

Figure Analogy: A : B :: C : ? Figure A is enlarged by 2× to become Figure B. What should Figure '?' look like when the same scaling is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Scaling Factor
- Figure A square: 25 units
- Figure B square: 50 units
- Scaling factor = 50/25 = 2

STEP 2: Apply to Figure C
- Figure C: Circle
- Apply scaling factor 2
- New dimensions = original × 2

STEP 3: Verify
- Shape type preserved ✓
- Proportions preserved ✓
- Only size changed ✓

Answer: Circle enlarged by 2×
scaling, size-change, proportional
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