Shape Analogies

An analogy question shows you how one shape changes into another, and then asks you to apply the same change to a new shape. Think of it as "Shape A is to Shape B as Shape C is to ?" Your job is to work out the transformation and use it to find the answer.

Analogies are a popular question type across all 11+ exams, and CEM papers can make them especially challenging by using abstract shapes and multiple simultaneous changes.

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How Analogy Questions Work

You are given a pair of shapes (A and B) and a third shape (C). You need to find the shape that should go with C, based on the same relationship that connects A to B.

Given pair	Your task
Shape A changes to Shape B	Shape C changes to ?

Simple Example

Shape A	Shape B	Shape C	Answer
Large black circle	Small black circle	Large black square	Small black square

Rule: The shape gets smaller. Everything else stays the same.

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Types of Transformation

Here are the main ways a shape can change in an analogy:

1. Size Change

Before	After
Large	Small
Small	Large

2. Shading Change

Before	After
Black (solid)	White (empty)
Striped	Solid
Grey	Black

3. Rotation

Before	After	Transformation
Arrow pointing up	Arrow pointing right	90 degrees clockwise
Arrow pointing up	Arrow pointing down	180 degrees

4. Reflection (Mirror Image)

The shape is flipped over a line, creating a mirror image. Left and right swap (for a horizontal reflection) or top and bottom swap (for a vertical reflection).

5. Shape Type Change

Before	After	Rule
Triangle (3 sides)	Square (4 sides)	Add 1 side
Pentagon (5 sides)	Hexagon (6 sides)	Add 1 side

6. Adding or Removing Elements

Before	After
Circle with no dot	Circle with a dot in the centre
Square with 2 lines inside	Square with 3 lines inside

7. Position Change

A dot or inner shape moves from one position to another (e.g. from the top to the bottom of the main shape).

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Worked Example 1 — Single Transformation

Shape A	Shape B	Shape C	Answer
White triangle	Black triangle	White hexagon	?

Step 1: Compare A and B. The shape stays the same (triangle). The shading changes from white to black.

Step 2: Apply the same change to C. White hexagon becomes black hexagon.

Answer: Black hexagon.

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Worked Example 2 — Two Transformations

Shape A	Shape B	Shape C	Answer
Large white circle	Small black circle	Large white square	?