4.2 Shape Analogies, Similarities & Odd One Out
Key Takeaways
- Shape analogies present a transformation pair (Shape A to Shape B) and require applying the exact same mapping vector to derive the missing target shape (Shape C to Shape D).
- Common analogy transformations include outer-inner shape swapping, line style changes (solid to dashed), 90° or 180° rotations, line reflection, and shading reversal.
- Odd One Out items require identifying an underlying geometric invariant shared by 4 out of 5 shapes, such as line symmetry count, line crossing nodes, or angle types.
- Similarities items require identifying the rule a set shares before testing options, and countable rules such as sides, enclosed regions or lines of symmetry should be tried before subjective ones.
- Distractor elimination in classification items relies on validating the candidate rule across all remaining shapes rather than selecting an option based on subjective visual complexity.
Shape Analogies, Similarities & Odd One Out
Visual classification items evaluate a student's ability to abstract geometric properties, identify relationships between pairs of shapes, and discover invariant rules within sets of figures. In GL Assessment Kent Test papers, these questions appear in three primary formats: Shape Analogies, Odd One Out / Similarities, and Code-to-Shape Matching.
Shape Analogies: The A is to B as C is to ? Framework
Shape analogies present a relationships pair (Shape A and Shape B), followed by a third shape (Shape C) and five option choices. The candidate must determine the transformation rule that converts A into B, and apply that identical rule vector $\vec{T}$ to C to yield Shape D.
| Analogy Transformation Type | Visual Mechanism | Exam Example |
|---|---|---|
| Inversion & Role Swap | Outer container and inner element swap places and scale. | Large square with inner circle $\rightarrow$ Large circle with inner square. |
| Shading Reversal | Black fills become white, white fills become striped or black. | Black triangle with white border $\rightarrow$ White triangle with black border. |
| Line & Border Mutation | Solid border lines change to dashed, dotted, or double lines. | Solid pentagon $\rightarrow$ Dashed pentagon. |
| Combined Spatial Shift | Planar rotation paired with reflective flipping. | Arrow pointing UP $\rightarrow$ Rotated $90^\circ$ CW and reflected horizontally. |
| Element Split & Multiply | Single shape splits into two smaller identical shapes. | 1 large star $\rightarrow$ 2 small stars positioned horizontally. |
Step-by-Step Analogy Solution Methodology
- Analyze A $\rightarrow$ B Transformation: List every distinct attribute change between Shape A and Shape B (e.g., Rule 1: Rotate $90^\circ$ CW; Rule 2: Invert shading; Rule 3: Add 1 internal dot).
- Apply Rule 1 to Shape C: Execute the first transformation on Shape C and scan answer choices to eliminate invalid options.
- Apply Rule 2 and Rule 3: Filter remaining options through secondary rules until only one option satisfies the complete transformation vector.
Odd One Out & Shape Similarities
Odd One Out questions present 5 shapes. Four of the shapes share a strict geometric property (the invariant rule), while one shape violates this rule (the Odd One Out).
Common Invariant Geometric Properties
- Symmetry & Axes: Four shapes have an even number of reflection symmetry lines (e.g., 2 or 4), while the odd shape has an odd number (e.g., 1 or 3).
- Rotational Order: Four shapes possess rotational symmetry order $> 1$, while the odd shape has no rotational symmetry (order 1).
- Line Crossing & Nodes: Four figures consist of paths that intersect exactly twice, while the odd figure intersects three times.
- Relative Spatial Contact: In four figures, a small black dot touches a straight edge; in the odd figure, the dot touches a curved edge or vertex corner.
- Enclosed Regions: Four shapes are divided into an odd number of closed internal regions (e.g., 3 or 5), while the odd shape has an even number (e.g., 4).
[!IMPORTANT] The Rule of Four Verification: Never select an answer choice simply because it "looks unusual" or "more complex". You MUST explicitly state the rule that connects the other FOUR shapes together. If you cannot state a unifying rule for four shapes, your hypothesis for the odd shape is invalid.
Similarities: Finding the Rule a Set Shares
The mirror image of odd one out is the similarities item: a set of figures shares one property, and you must choose the further figure that also has it. The danger is different. In odd one out you are looking for the one that breaks a rule; here you must first identify the rule, and the set is deliberately varied in every other respect so that surface features cannot help.
Method. State a candidate rule in words after looking at the first two figures, then test it against the third. If it survives, test it against each option and keep the option it accepts. If it fails, discard it completely rather than patching it — a patched rule ("mostly curved edges, except that one") is almost always the wrong rule.
Rules that sets are built on, in rough order of frequency:
| Rule family | What to check |
|---|---|
| Count | Number of sides, dots, lines, enclosed regions, or intersections |
| Symmetry | Number of lines of symmetry, or order of rotational symmetry |
| Relationship | Inner shape has half the sides of the outer; shading matches the smaller element |
| Contact | Whether elements touch, overlap, or stay separate |
| Proportion | Fraction of the figure shaded; ratio of large to small elements |
Worked example. Three figures each contain a large shape with a small shape inside it: a hexagon containing a triangle, a square containing a two-sided arc, an octagon containing a square. The rule is not "polygons" or "shading" — it is the inner shape has half as many sides as the outer. Only an option obeying that relationship is correct.
The counting rules are the ones to try first, because they are objective. "Looks more complex" is not a rule and cannot be tested.
Shape codes, where each figure carries a two- or three-letter label, use closely related decoding logic and are covered in full in section 4.6.
Exam Traps & Time-Saving Tactics
- The Superficial Similarity Trap: Distractor shapes often share cosmetic features (like color or size) with Shape A, but fail the structural transformation rule. Always prioritize geometry over superficial appearance.
- Letter Order Mixing: In code questions, ensure you do not reverse position meanings (e.g., mistaking the 1st letter rule for the 2nd letter rule).
Shape A is a large white triangle containing a small black circle inside it. Shape B is a large black circle containing a small white triangle inside it. Shape C is a large striped pentagon containing a small solid black square inside it. Applying the identical transformation vector to Shape C, what is Shape D?
You are presented with 5 shapes to solve an Odd One Out item: Shape 1 is a regular hexagon (6 sides, 6 lines of symmetry). Shape 2 is an equilateral triangle (3 sides, 3 lines of symmetry). Shape 3 is a square (4 sides, 4 lines of symmetry). Shape 4 is a rectangle with unequal adjacent sides (4 sides, 2 lines of symmetry). Shape 5 is a regular pentagon (5 sides, 5 lines of symmetry). Which shape is the Odd One Out and why?
A similarities set shows a hexagon containing a triangle, a square containing a two-sided arc figure, and an octagon containing a square. What rule do they share?
Set A consists of three geometric figures that all share a specific underlying property: Figure 1 has 2 pairs of parallel lines and 4 right angles (rectangle). Figure 2 has 2 pairs of parallel lines and 0 right angles (rhombus). Figure 3 has 3 pairs of parallel lines (regular hexagon). Which of the following test shapes belongs to Set A?