Spatial Visualisation

Spatial visualisation is the ability to picture shapes, movements, and transformations in your head. It is the master skill behind every NVR question type. This lesson focuses on building that skill through specific question types: hidden shapes, counting shapes, fitting shapes together, and completing symmetrical figures.

---

Hidden Shapes (Embedded Figures)

In these questions you are shown a simple target shape and asked to find it hidden inside a more complex figure.

How It Works

Target shape	Complex figure
A small right-angled triangle	A geometric pattern made of many overlapping lines and angles

You must identify exactly where the target shape sits within the complex figure.

Strategy

1. Study the target shape carefully. Note its proportions, angles, and relative sizes of its sides.
2. Scan the complex figure for lines that could form the sides of the target shape.
3. Check orientation. The hidden shape may be rotated but usually it is not reflected.
4. Verify every side. Each side of the target shape must lie exactly along a line in the complex figure.

Worked Example

Target shape: An isosceles triangle (two equal sides, one shorter base).

Complex figure: A large square divided by its two diagonals (forming an X inside the square), with a horizontal line through the centre.

Finding the target: Look at the top half of the figure. The two diagonal lines from the top corners meet at the centre, and the horizontal line forms the base. This creates an isosceles triangle. The target shape is hidden in the top half of the figure.

---

Counting Shapes

These questions show you a complex figure and ask "How many triangles (or rectangles, or squares) can you find?"

Why the Count Is Larger Than You Expect

Small shapes can combine to form larger versions of the same shape. For example, two small triangles side by side might form one large triangle.

Systematic Method

1. Label each small section of the figure (A, B, C, D, etc.).
2. Count individual shapes. How many single sections are the target shape?
3. Count combinations of 2. Which pairs of adjacent sections form the target shape?
4. Count combinations of 3, 4, etc. Continue until you have checked all possible combinations.
5. Add up the totals.

Worked Example

A large triangle is divided into 4 smaller triangles by connecting the midpoints of each side.

Type	Count
Small triangles (single sections)	4
Medium triangles (2 small triangles combined)	0 (in this particular layout, two small triangles do not form a triangle)
Large triangle (all 4 combined)	1
Inverted central triangle	1 (the upside-down triangle in the middle)
Total triangles	5

Wait — let us count more carefully. The 4 small triangles are: 3 pointing up at the corners, and 1 pointing down in the centre. Combining the centre triangle with each corner triangle gives 3 more medium triangles. Plus the large outer triangle. Total = 4 + 3 + 1 = 8.

Lesson: Always be systematic. It is easy to miss combined shapes if you count casually.

---

Fitting Shapes Together (Jigsaws)

These questions show you an outline shape and ask which combination of smaller shapes would fit together to fill it exactly.

Strategy