Shape Construction and Grouping of Identical Figures: Types, Methods and Examples
This chapter joins two closely related non-verbal reasoning topics. In shape construction, two or more pieces or figures are given and the candidate must find the shape that can be formed by joining them, or must choose the pieces that make a given shape. In grouping of identical figures, nine figures are given and the candidate must divide them into three groups of three, where the figures in each group share a common property.
Both topics are asked in APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations because they test spatial imagination and the ability to compare shapes by their parts rather than by their overall look. There is no calculation; the work is done by matching edges, noting the number of sides and observing what the figures have in common. This article gives a complete deep-study revision of shape construction and grouping of figures: the basic terms, the core rules, the types of questions, the step-by-step method, the common mistakes and a practical preparation plan.
Basic Terms
- Shape construction: forming a complete figure by joining the given pieces.
- Component piece: a part of the final shape, such as a triangle or a semicircle.
- Joining edge: the side along which two pieces meet.
- Silhouette: the outer outline of a shape without its inner lines.
- Identical figures: figures that are exactly the same in shape and size.
- Common property: the feature, such as the number of sides or curves, shared by every figure of a group.
- Grouping: dividing the given figures into classes on the basis of a common property.
- Three classes: the three groups of three figures required in a grouping question.
- Line symmetry: a shape that can be divided into two matching halves.
- Curved figure: a figure made with curved lines such as circles and arcs.
- Straight-line figure: a figure made only of straight lines.
- Open figure: a figure whose lines do not enclose an area.
- Closed figure: a figure whose lines enclose an area.
Core Concepts and Rules
- The pieces given for construction keep their size and shape; only their positions change while joining.
- The outer outline of the final shape must be produced exactly by the given pieces, with no gap and no overlap.
- Count the number of sides and curves of the pieces before choosing the answer; the count rarely changes.
- In grouping, every figure of a group must satisfy the common property, and no two groups may share the same property.
- The simplest properties are the number of sides, the number of curves, the number of parts and the type of symmetry.
- Closed and open figures, straight and curved lines, and shaded and unshaded regions are common grouping properties.
- The overall look of a figure can mislead, so always compare by the parts and by the outline.
- Rotation of a piece is usually allowed in construction, but changing its shape or size is not.
- In a grouping question, first find one clear property for three figures and remove them, then group the rest.
- If two figures look identical, compare their exact edges, because one may hide a small difference.
Types of Shape Construction and Grouping Questions
The first type gives two or more pieces and asks which figure they form. The second type gives a figure and asks which set of pieces can build it. The third type gives nine figures and asks for the three groups of three identical figures. The fourth type gives a set of figures and asks which one is different from the rest. The fifth type gives pieces in different orientations and asks whether a given shape can be made from them, and the sixth type gives a shaded design built from several parts and asks how many of a particular part it contains.
Steps to Solve a Shape Construction and Grouping Question
For construction, first count the sides and curves of every piece and note the joining edges. Second, imagine the pieces brought together along a matching edge and trace the outer outline. Third, compare that outline with each option and reject any option with a missing side or an extra line. Fourth, choose the option whose outline is made exactly by the given pieces.
For grouping, first look at all the figures and note the features that differ, such as straight or curved lines, closed or open shape, number of sides and type of symmetry. Second, pick any figure and search for two others sharing a clear property. Third, set those three aside as one group. Fourth, continue with the remaining six until three groups are formed. Finally, check that each group has exactly three figures and that no figure is left ungrouped.
Examination Trends
In competitive examinations these topics usually carry two to four marks. Shape construction questions commonly use triangles, semicircles, quarters of circles and small squares, and the answer is a simple closed shape such as a circle, a square or a star. Grouping questions usually use nine figures built from combinations of lines and curves, and the common properties are the number of sides, the number of curves, the type of symmetry and whether the figure is open or closed. Because the topics depend on observation, regular practice makes them both quick and accurate.
Common Mistakes to Avoid
- Do not change the size or shape of a piece to make it fit.
- Do not accept a shape whose outline leaves a gap or needs an extra line.
- Do not group figures by their overall look; use a clear common property.
- Do not form a group of figures that share more than one property, because another group will then fail.
- Do not forget to use all the given pieces in a construction question.
- Do not leave any figure ungrouped or place four figures in one group.
How to Prepare This Topic
Begin with paper cut-outs of triangles, squares and semicircles and try to join them into larger shapes. This makes the behaviour of the joining edges very clear. Then move to the printed construction questions and solve them by imagining the same joins. For grouping, take a set of figures and write down the number of sides and curves beside each one before deciding the groups.
A very useful habit is to look only at the outline while solving construction questions, ignoring the internal lines, and to look only at the common property while solving grouping questions, ignoring the overall picture. Another good method is to check the answer by rebuilding the shape mentally from the pieces, which catches almost every mistake. Daily practice of fifteen to twenty questions for a few days makes the topics quick and reliable, and the same skills help in figure matrix, paper folding and mirror image questions.
Quick Revision Tips
- Count the sides and curves of every piece before choosing the answer.
- Match the joining edges and trace the outer outline only.
- Use all the pieces without changing their size or shape.
- In grouping, fix one clear common property and remove three figures at a time.
- Keep the properties of the groups different from one another.
- Check at the end that every figure is used exactly once.
Final Revision Note
In the final revision, solve ten construction and ten grouping questions and note which shapes or properties confused you. Rebuild those shapes with cut-outs or in the mind and regroup the confusing figures slowly. This active rebuilding is exactly what the examination tests, and with regular practice shape construction and grouping of figures become fast and dependable.
Frequently Asked Questions
What is shape construction in reasoning?
It is a topic in which given pieces are joined to form a complete shape, or the pieces that build a given shape are chosen.
What is grouping of identical figures?
It is a topic in which nine figures are divided into three groups of three on the basis of a common property that the figures of a group share.
Can the pieces be rotated while joining?
Rotation is usually allowed, but the shape and size of a piece must not be changed; only its position may change.
How do I choose the common property for grouping?
Look at the number of sides, the number of curves, the type of symmetry and whether the figure is open or closed.
Which exams ask these questions?
APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations ask shape construction and grouping questions in the non-verbal reasoning section.