All free lessons / Non-Verbal Reasoning / NVR: hidden shapes
Non-Verbal Reasoning · Visual patterns
NVR: hidden shapes
A free preview from the Athena Learning Library — the same lesson registered students learn from.
In this lesson: Find a target triangle hidden, at the same size, inside a busier line picture.
Before you start
Camouflage hides an animal against a busy background. Here a triangle hides inside a tangle of lines — and it can only hide where its three sides already exist.
Watch it happen
Find the hidden triangle
Meet the target: a triangle whose sides are about 2.2, 4.1, 4.2 units long. Study its shape — long side, short side, and the corner between them.
The idea
In a hidden-shapes question, a small target shape is hiding inside a bigger, busier picture. The hidden copy is always exactly the same size as the target and turned the same way. It is never bigger, smaller, rotated or flipped, even though its lines may be shared with other shapes.
Work systematically. First, study the target: count its sides, note its angles, and remember one special feature, such as its longest side. Next, scan the big picture slowly, part by part, looking for that longest side or a matching corner. When you find a possible match, trace the rest of the target's outline in your mind, side by side, without lifting off.
The trick is that the hidden shape's edges may be made from pieces of several different lines, and extra lines may cross through it. A shape that looks almost right but is turned or stretched is wrong. If a section of the picture has no match, cross it off mentally and move on, rather than staring at the whole picture and hoping the shape jumps out.
Worked example
The triangle at the top is hidden, complete and at exactly the same size, inside one of the four pictures. Which one?
- Meet the target on its own first: a triangle with sides about 2.0, 5.0, 6.7. Its longest side rises from left to right, its middle side rises from left to right and its shortest side stands upright. Fix that exact shape in your mind — the hidden copy is the same size, never stretched or shrunk.
- Now look at the four pictures. In each one, hunt for the target's longest side first: a line of exactly that length, lying the same way. Pictures without it are out at once.
- For each picture still standing, check the other two sides can be traced along lines already drawn, meeting at the right corners. One missing side kills the picture.
- Only picture A passes every check: all three sides are really there, traced in colour in the last picture.
Answer: Picture A — Trace the three sides of the top triangle (2.0, 5.0, 6.7 units) in each picture. Only in picture A do all three sides appear as complete straight lines already drawn in the picture. In the other pictures at least one side is missing or the wrong length.
Try one yourself
New hunt, same method: the target triangle at the top is hidden in one of the four pictures. Which one — A, B, C or D?
Watch out
- Accepting a copy that is the right shape but turned or a different size — both are wrong in this question type.
- Rejecting the true copy because extra lines cross it or its sides are shared with other shapes.
- Staring at the whole picture; work section by section and cross off areas you have checked.
Quick check
Try these on your own first — then reveal each answer.
1. The target triangle at the top is hidden in one of these four pictures. Which one?
2. The target triangle at the top is hidden in one of these four pictures. Which one?
Practise this concept
Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.