How to solve Figure Classification questions

Figure Classification asks you to find a property shared by a group of figures and choose the answer that belongs in that group. The official TACHS handbook includes this family among its Ability samples. The original examples below teach how to test a property across all the figures and choices.

This is different from completing a matrix. You are not necessarily looking for a change from left to right. You are finding something that remains true even when the shapes, positions, or sizes vary. The question becomes manageable when you can state that shared property precisely.

Compare every group member

Start by describing the visible features. Count parts, inspect open and closed regions, and note how one part relates to another. An inner shape may touch an outer boundary, lie entirely inside it, or sit outside it. Those relationships can matter more than the particular shape names.

Then ask what changes among the given figures. If one group member is a triangle and another is a circle, being a triangle cannot be the common property. Differences can help eliminate a weak rule before you spend time testing answer choices.

A rule should explain all of the group, not merely the most noticeable figure. If it needs an exception for a displayed member, reconsider it. Choose the smallest clear description that accounts for the relevant information rather than a complicated story about the pictures.

Worked example 1: A relationship between two shapes

Look at the three figures in the group. Which choice belongs with them? Compare the small circle in each figure with the shape around it.

The answer is B. Each group figure contains exactly one small circle completely inside a larger closed shape. The small circle does not touch the outer boundary. B follows the same rule, even though its outer shape is a diamond.

A places the small circle outside the larger figure. C has two small circles inside rather than one. D has no small circle. E puts its small circle across the boundary, so it is not completely inside. Only B satisfies the whole description.

Choosing the option whose outer shape looks most familiar would not solve the task. The given outer shapes already vary. Their variation tells you to inspect a relationship that survives a change in outer shape, while keeping the smaller circle’s number and position consistent.

You can verify the key without relying on resemblance. For every displayed member, count one small circle and check that its entire circumference lies inside the boundary. Repeat that same check on A through E. B alone passes both parts.

Worked example 2: Equal division through the center

The next group uses circles with straight dividing lines. Choose the answer that shares the group’s property. Here the outer circle stays the same, while the direction of the dividing line changes.

The answer is E. Each group circle has exactly one straight line passing through its center and ending on the circle at both ends. That line divides the circle into two equal halves. E shows another diameter, at a different angle, and satisfies the rule.

A’s vertical line is off-center, so its two regions have unequal areas. B has two full dividing lines, creating four regions. C’s line starts at the center and reaches the boundary only once, so it does not split the whole disk into two regions. D’s chord is off-center. Only E has one complete central division.

The orientation is allowed to vary because it already varies among the group members. The location of the line relative to the center is not allowed to vary: it is constant in the group. This distinction explains why a tilted correct answer beats an upright but off-center distractor.

To check the geometry, remember that a line through the center of a circle creates two semicircles. Rotating that diameter preserves the equal halves. Moving the line away from the center makes one region smaller and breaks the shared property.

Make your rule specific enough to reject choices

A first description such as “all contain shapes” is true but too broad. It does not separate the intended answer from the alternatives. Improve the description until it includes the useful count, location, or relationship shown by every group member.

On the other hand, avoid adding details that the group does not keep constant. In the first example, requiring a square outer shape would reject valid group members. In the second, requiring a vertical line would do the same. A correct explanation includes the invariant feature and allows the demonstrated variations.

The answer choices can help reveal an overlooked distinction, but do not let one choice dictate the rule. If your proposed rule selects two answers, compare those answers and look back at the group for the feature that decides between them.

Explain each wrong choice during review

Review becomes more useful when you identify the precise reason each distractor fails. A statement such as “A is outside rather than inside” teaches a check that can be repeated. “B looks right” does not explain why any other option is wrong.

If you repeatedly miss count rules, practice with a few groups that vary shape while keeping count constant. If you miss relationship rules, compare figures that differ only in touching, crossing, or containment. Keep the first practice sets focused enough to make the missed feature visible.

After that, mix different tasks so that the student must discover which feature matters. Knowing in advance that every question is about counting can hide a weakness in choosing a rule. Mixed practice tests that decision more directly.

Practice reasoning before speed

Begin with untimed examples and complete explanations. Once the method is understood, use timed sets and review the questions where a vague rule consumed time. A brief, testable description can help you move more efficiently than repeatedly comparing overall appearances.

TACHS Prep uses an estimated 22 Figure Classification questions in ten standard-time minutes. Those are practice settings based on public information, not official per-part counts or time limits. The six-part guide explains the complete practice model.

Keep the three picture tasks distinct. In Figure Matrices, you complete relationships in a grid. In Paper Folding, you reverse physical folds. In classification, you find the property that every group member shares and choose the one answer that preserves it.