5.1 Figural Analogies (Visual Relationships)

Figural Analogies (Visual Relationships)

Figural analogies test your ability to recognize relationships between visual objects and apply that identical relationship to a new set of objects. If you've ever seen a verbal analogy like "Hot is to Cold as Day is to Night," a figural analogy works exactly the same way, but it uses geometric shapes, patterns, and spatial relationships instead of words.

In a standard figural analogy problem, you are presented with a pair of figures that have a specific relationship. You are then given a third figure and asked to select a fourth figure from a set of multiple-choice options so that the relationship between the third and fourth figures matches the relationship between the first and second.

The Anatomy of a Figural Analogy

The most common format is a 2x2 matrix or a linear sequence presented as A : B :: C : ?.

• Figure A transforms into Figure B according to a specific rule.
• Figure C must transform into the unknown Figure D using the exact same rule.

To succeed, you must become highly observant of the various types of transformations that can occur. Often, the OLSAT Level G will combine two or three different transformations in a single problem to increase the difficulty.

Types of Visual Transformations

When analyzing the transition from Figure A to Figure B, look for the following common transformations:

1. Rotation and Reflection

• Rotation: The figure or its components may rotate clockwise or counterclockwise. Common rotation angles are 45°, 90°, and 180°. Always track a specific point on the figure to determine the degree and direction of rotation.
• Reflection (Flipping): The figure may be flipped across a vertical, horizontal, or diagonal axis. A reflection often looks like a rotation, but if the figure is asymmetric, a reflection will create a mirror image that cannot be achieved through simple rotation.

2. Size and Proportion Changes

• Scaling: The entire figure may shrink or grow.
• Relative Sizing: One part of the figure may grow while another part shrinks. For instance, a large circle with a small square inside might transform into a small circle with a large square inside.

3. Shading and Color Reversals

• Shading Shifts: Elements may change from white to black, black to grey, or white to a patterned shading (like stripes or dots).
• Inversion: A completely black figure with white dots may invert to become a white figure with black dots. Always check if the shading change is absolute or conditional (e.g., "only the overlapping sections turn black").

4. Addition, Deletion, and Substitution

• Addition: A new element (a line, a dot, a border) is added to the figure.
• Deletion: An existing element is removed.
• Substitution: A specific shape is swapped out for another (e.g., all circles become triangles).

5. Spatial Reorganization and Overlap

• Positioning: Elements may swap places. For example, the top element moves to the bottom, and the bottom element moves to the top.
• Intersection: Shapes that were separated may move together to overlap, or overlapping shapes may separate. Pay close attention to what happens to the overlapping region—does it disappear, turn a different color, or create a new shape?

The Systematic Approach to Figural Analogies

To avoid getting tricked by "distractor" answer choices, you must adopt a rigorous, step-by-step approach. Do not simply look at Figure C and then scan the answers for something that "looks right."

Step 1: Deconstruct Figure A

Break Figure A down into its component parts. Is there an outer shape? An inner shape? A specific line thickness? A distinct shading pattern? List these elements mentally.

Step 2: Formulate the Verbal Rule

Examine how each component changes from Figure A to Figure B. Speak the rule in your mind as clearly as possible. Example Rule: "The outer shape remains the same size but rotates 90 degrees clockwise. The inner shape shrinks by half, turns from white to black, and moves from the center to the top right corner."

Step 3: Apply the Rule to Figure C

Before looking at the answer choices, mentally apply your precise verbal rule to Figure C. Imagine what Figure D should look like. Example Application: "Figure C has an outer hexagon and an inner triangle. The hexagon must rotate 90 degrees clockwise. The triangle must shrink, turn black, and move to the top right corner."

Step 4: Eliminate and Select

Now look at the answer choices. Eliminate any option that violates even one part of your rule. The correct answer must satisfy every single condition of the transformation.

Advanced Strategies for Level G

At the Level G tier, the test designers will intentionally create answer choices that satisfy most of the rule, but not all of it. For example, if the rule dictates a 90-degree rotation and a shading inversion, an incorrect distractor might show the correct rotation but fail to invert the shading.

Furthermore, sometimes the relationship is not A -> B, but rather A -> C. If you cannot find a logical rule connecting Figure A to Figure B, look to see if Figure A is related to Figure C. If so, Figure B will be related to Figure D in the same way. This is known as an "alternating analogy" and is a common curveball on advanced spatial reasoning tests.