Overlapping Shapes

In overlapping shapes questions, two or more shapes are placed on top of each other, and you must work out what the combined image looks like — or work backwards from a combined image to identify the original shapes. This question type tests your ability to mentally layer transparent images and track every element carefully.

---

How Overlapping Works

Imagine each shape is drawn on a transparent sheet (like tracing paper). When you stack the sheets, you see everything from both shapes combined into one image.

Simple Example

Shape A	Shape B	Combined (A + B)
A circle on the left side	A square on the right side	A circle on the left AND a square on the right

Since the shapes do not overlap, the combined image is simply both shapes side by side.

Overlapping Example

Shape A	Shape B	Combined (A + B)
A vertical line through the centre	A horizontal line through the centre	A plus sign (+)

When the shapes overlap in the centre, their lines combine to form a new pattern.

---

Types of Overlapping Questions

Type 1: Combining Two Shapes

You are given two separate shapes and asked which answer option shows the correct combined image.

Strategy:

1. List every element in Shape A (outlines, lines, dots, fills).
2. List every element in Shape B.
3. Mentally stack them. Every element from both shapes should appear in the combined image.
4. Pay attention to positions. Elements must be in exactly the right positions.
5. Check for overlaps. Where elements from both shapes occupy the same position, they merge (e.g. two overlapping circles become one circle).

Type 2: Breaking Down a Combined Image

You are shown a combined image and must identify which pair of original shapes could have produced it.

Strategy:

1. Identify all elements in the combined image.
2. For each answer option, check whether the two given shapes contain exactly the right elements to produce the combined image.
3. Every element must be accounted for — nothing extra, nothing missing.

---

Worked Example 1 — Simple Combination

Shape A	Shape B
A triangle with a dot in the top-left corner	An empty circle in the centre

Combined image: A triangle with a dot in the top-left corner and a circle in the centre. The circle overlaps the interior of the triangle.

---

Worked Example 2 — Lines Overlapping

Shape A	Shape B
Two diagonal lines forming an "X" shape	A square outline

Combined image: A square with an X inside it (the diagonals of the square).

---

Worked Example 3 — Breaking Down

Combined image: A circle with a horizontal line through the middle and a small dot above the line.

Which pair of shapes made this?