Ready to master figure analogy? This concept mastery features 20 beginner-level challenges. Worksheet 2 of 30 sharpens your shape relationships skills. Master shape relationships, image analogies, graphical comparisons through guided practice. Perfect for entry-level test preparation.
STEP 2: Apply to Figure C - C: 2 dot(s) (different container) - Add 2 more dot(s) - Result: 4 dots total
Answer: Square with 4 dots (2 more than original)
Question 3
Figure Analogy: A : B :: C : ?
Figure A is reflected across a horizontal axis to become Figure B.
Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:
STEP 1: Identify Mirror Axis - Compare A and B: They are mirror images - Mirror axis: Horizontal
STEP 2: Properties of horizontal Mirror - Horizontal mirror: Left ↔ Right swap - All horizontal positions inverted - Vertical positions unchanged
STEP 3: Apply to Figure C - Reflect C across horizontal axis - Maintain shape type - Invert orientation
Answer: Figure mirrored across horizontal axis (mirror image of C)
Question 4
Figure Analogy: A : B :: C : ?
In A→B, elements swap positions (left element moves right, right element moves left). Apply to C.
Step-by-Step Solution:
STEP 1: Map Element Positions in A - Container: Square - Element 1 (Circle): Left portion of square - Element 2 (Triangle): Right portion of square - Spatial arrangement: Circle | Triangle (left | right)
STEP 2: Map Element Positions in B - Container: Square (same) - Element 1 (Triangle): Left portion of square - Element 2 (Circle): Right portion of square - Spatial arrangement: Triangle | Circle (left | right)
STEP 3: Identify Transformation Type - Container: Unchanged (square remains square) - Element types: Unchanged (circle and triangle still present) - Element positions: Swapped (exchanged positions) - Transformation: Positional swap/exchange
STEP 4: Identify Elements in C - Container: Circle - Element 1 (Square): Left portion of circle - Element 2 (Line): Right portion of circle - Current arrangement: Square | Line (left | right)
STEP 5: Apply Position Swap to C - Element 1 (Square): Moves from left → right - Element 2 (Line): Moves from right → left - Result arrangement: Line | Square (left | right) - Container: Remains circle (unchanged)
Answer: Circle with line on left portion and square on right portion (positions swapped)
Question 5
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
Question 6
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)
Question 7
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)
Question 8
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: Square with inscribed square (inner becomes square)
Question 9
Figure Analogy: A : B :: C : ?
Figure A is reflected across a horizontal axis to become Figure B.
Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:
STEP 1: Identify Mirror Axis - Compare A and B: They are mirror images - Mirror axis: Horizontal
STEP 2: Properties of horizontal Mirror - Horizontal mirror: Left ↔ Right swap - All horizontal positions inverted - Vertical positions unchanged
STEP 3: Apply to Figure C - Reflect C across horizontal axis - Maintain shape type - Invert orientation
Answer: Figure mirrored across horizontal axis (mirror image of C)
Question 10
Figure Analogy: A : B :: C : ?
In A→B, elements swap positions (left element moves right, right element moves left). Apply to C.
Step-by-Step Solution:
STEP 1: Map Element Positions in A - Container: Square - Element 1 (Circle): Left portion of square - Element 2 (Triangle): Right portion of square - Spatial arrangement: Circle | Triangle (left | right)
STEP 2: Map Element Positions in B - Container: Square (same) - Element 1 (Triangle): Left portion of square - Element 2 (Circle): Right portion of square - Spatial arrangement: Triangle | Circle (left | right)
STEP 3: Identify Transformation Type - Container: Unchanged (square remains square) - Element types: Unchanged (circle and triangle still present) - Element positions: Swapped (exchanged positions) - Transformation: Positional swap/exchange
STEP 4: Identify Elements in C - Container: Circle - Element 1 (Square): Left portion of circle - Element 2 (Line): Right portion of circle - Current arrangement: Square | Line (left | right)
STEP 5: Apply Position Swap to C - Element 1 (Square): Moves from left → right - Element 2 (Line): Moves from right → left - Result arrangement: Line | Square (left | right) - Container: Remains circle (unchanged)
Answer: Circle with line on left portion and square on right portion (positions swapped)
Question 11
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)
Question 12
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: Circle with inverted shading
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
Question 14
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 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.
Question 15
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 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.
Question 16
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)
Question 17
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 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.
Question 18
Figure Analogy: A : B :: C : ?
Figure A is reflected across a vertical axis to become Figure B.
Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:
STEP 1: Identify Mirror Axis - Compare A and B: They are mirror images - Mirror axis: Vertical
STEP 2: Properties of vertical Mirror - Vertical mirror: Left ↔ Right swap - All horizontal positions inverted - Vertical positions unchanged
STEP 3: Apply to Figure C - Reflect C across vertical axis - Maintain shape type - Invert orientation
Answer: Figure mirrored across vertical axis (mirror image of C)
Question 19
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
Question 20
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)