Select the answer choice that follows the same classification rule - TACHS Ability

SECTION 1

Why Do We Classify Figures?

Humans have been sorting and grouping things for thousands of years. Early scientists grouped animals, plants, and minerals by their shared features. Classification (putting things into groups based on shared traits) is one of the most important thinking skills you can develop. On the TACHS exam, figure classification questions test your ability to find patterns in shapes and pick the answer that fits the same rule.

350 BC • Aristotle's Categories

The Greek philosopher Aristotle grouped living things by their traits. This was one of the first uses of classification in science.

1735 • Linnaeus Creates Taxonomy

Carl Linnaeus invented a system to classify every living thing. He sorted organisms by shared features, much like we sort figures today.

1900s • IQ and Aptitude Tests

Psychologists began using shape puzzles to measure reasoning ability. These tests showed that finding patterns is a key part of intelligence.

Today • The TACHS Exam

Figure classification questions appear on the TACHS to see how well you can spot rules and patterns among groups of shapes.

The big question these problems ask is simple: "What do these figures have in common, and which answer choice shares that same trait?" Let's learn how to answer that question every time.

SECTION 2

Core Principles of Figure Classification

Every figure classification question gives you a group of three figures. These figures all follow a hidden rule. Your job is to figure out that rule and then pick the answer choice that also follows it. Here are the core ideas you need to know.

Identify Visual Attributes

Look at each figure's shape, size, shading (filled, empty, striped), number of sides, and orientation (which way it faces).

Find the Common Rule

Ask yourself: what do ALL three figures share? The rule might involve one attribute (like "all are triangles") or a combination (like "all are small and shaded").

Test Each Answer Choice

Check every answer against your rule. The correct answer will match every part of the rule. Wrong answers will break at least one part.

Watch for Distractors

Some answer choices look similar but fail the rule in a sneaky way. Double-check details like shading, size, or the number of shapes inside a figure.

Eliminate Wrong Answers

If you are stuck, cross out any choice that clearly breaks the rule. This narrows your options and helps you find the right one.

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KEY TAKEAWAY

Think of figure classification like sorting laundry. You might sort clothes by color, size, or type. A sock doesn't go in the "shirts" pile, even if it's the same color. In the same way, the correct answer must match every part of the classification rule — not just one part.

SECTION 3

Seeing the Pattern: A Visual Guide

The diagram below shows a sample figure classification problem. Three figures share a rule, and you must pick which answer choice follows that same rule. Study the diagram and notice how the rule connects the group.

All three given figures are shaded triangles. Choice (A) is a shaded square — wrong shape. Choice (B) is an empty triangle — wrong shading. Choice (C) is a shaded triangle — it matches! Choice (D) is a shaded circle — wrong shape.

Notice how only one answer matches both parts of the rule: it must be a triangle and it must be shaded. This is why you always need to check every attribute before choosing your answer.

SECTION 4

How Figure Classification Works

Figure classification isn't about math equations. Instead, it's about a step-by-step thinking process. You can think of it like a checklist. For each figure in the given group, you examine specific attributes (features you can see). Then you find which attributes stay the same across all three figures. That consistent set of attributes is the classification rule.

The Six Attributes to Check

Attribute	What to Look For	Examples
Shape	What kind of figure is it?	Triangle, square, circle, pentagon, hexagon
Size	Is the figure big, medium, or small?	Large circle vs. small circle
Shading	Is it filled, empty, or patterned?	Solid black, white/empty, striped, dotted
Number of Sides	Count the straight edges.	3 sides, 4 sides, 5 sides, 0 sides (circle)
Orientation	Which direction does it face or point?	Pointing up, pointing right, rotated 45°
Inner Details	Are there lines, dots, or shapes inside?	A dot in the center, a line through the middle

Use this checklist every time you see a figure classification question.

Not every attribute will matter in every question. Sometimes the rule is just about shape. Other times it combines two or even three attributes. The key is to check all six attributes and narrow down which ones stay the same.

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PRO TIP

Start with the most obvious attribute first. If all three figures are the same shape, you've already found one part of the rule. Then check if size, shading, or other details also stay the same.

SECTION 5

Types of Classification Rules

Classification rules on the TACHS come in different levels of difficulty. Some rules use just one attribute, while harder questions combine multiple attributes. The diagram below shows the three main types of rules you'll see.

Single-attribute rules (green) are the easiest to spot. Two-attribute rules (yellow) require checking more features. Three-attribute rules (red) are the trickiest because you must match all three features at once.

When you first look at a problem, start by asking: "Are all the shapes the same?" If yes, shape is part of the rule. Then ask: "Are they all the same size?" Then: "Are they all shaded the same way?" Keep going through the six attributes until you find every part of the rule.

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WATCH OUT

Sometimes the three given figures are all different shapes, but they share something else — like they're all empty (not shaded), or they all have exactly four sides. Don't assume the rule is always about shape!

SECTION 6

Worked Example: Solving Step by Step

Let's walk through a complete example. Imagine you see three figures: a large empty square, a large empty circle, and a large empty triangle. The answer choices are: (A) a small empty square, (B) a large shaded circle, (C) a large empty hexagon, and (D) a large empty pentagon with a dot inside.

Finding the Classification Rule

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Step 1 — List Attributes of Each Given Figure

Figure 1: large, empty, square (4 sides). Figure 2: large, empty, circle (0 sides). Figure 3: large, empty, triangle (3 sides). Write these down so you can compare them.
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Step 2 — Find What Stays the Same

Shape? No — the shapes are all different (square, circle, triangle). Size? Yes — all three are large. Shading? Yes — all three are empty. Inner details? No special marks inside any of them.

Rule: All figures are large AND empty (with no inner details).
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Step 3 — Test Answer Choice (A)

Small empty square. Is it large? No, it's small. This breaks the rule.

(A) is eliminated.
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Step 4 — Test Answer Choice (B)

Large shaded circle. Is it large? Yes. Is it empty? No, it's shaded. This breaks the rule.

(B) is eliminated.
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Step 5 — Test Answer Choice (C)

Large empty hexagon. Is it large? Yes. Is it empty? Yes. Any inner details? No. It matches every part of the rule.

(C) is the correct answer! ✓
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Step 6 — Verify by Checking (D)

Large empty pentagon with a dot inside. Is it large? Yes. Is it empty? Yes. But it has a dot inside — an inner detail that none of the given figures have. This breaks the rule, confirming (C) is correct.

(D) is eliminated.

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KEY TAKEAWAY

Always check every answer choice, even after you think you found the right one. This is like double-checking your answer on a math test — it takes a few extra seconds but can save you from a careless mistake.

SECTION 7

Strategies, Strengths, and Common Mistakes

Some strategies work better than others on these questions. The table below compares helpful approaches with common mistakes students make. Use this as a guide to build good habits.

Winning Strategy ✓	Common Mistake ✗
Check all six attributes for every figure in the group before looking at the answers.	Only looking at shape and ignoring shading, size, or inner details.
Eliminate answer choices one at a time using the rule.	Picking the first answer that "looks right" without testing it.
Consider that the rule might combine two or three attributes.	Assuming the rule always involves just one attribute.
Look for what all three given figures share, not just what two of them share.	Building a rule from just two figures and ignoring the third.
Verify your answer by checking that all wrong choices break the rule.	Not checking the remaining choices after picking an answer.

Strategies vs. Mistakes

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REMEMBER

Think of yourself as a detective. You need evidence from all three figures before you can solve the case. If your rule doesn't fit one of the three figures, it's the wrong rule — go back and look again.

SECTION 8

Advanced Rules and Tricky Patterns

As you get better at figure classification, you'll encounter trickier rules. Some questions use patterns you might not expect. The table below compares basic rules with advanced ones you might see on harder problems.

Basic Rule	Advanced Rule	Why It's Harder
All shapes are circles.	All shapes have curved edges (circles, ovals, semicircles).	The rule is about a category of shapes, not one specific shape.
All shapes are shaded.	All shapes have the same pattern (stripes, dots, crosshatch).	You must notice the type of shading, not just whether it's shaded or not.
All shapes are the same.	Each figure contains two shapes (one inside the other).	You need to analyze the relationship between inner and outer shapes.
All shapes point up.	All shapes have a line of symmetry going left to right.	The rule is about a geometric property, not just direction.

Basic vs. Advanced Classification Rules

Don't worry if advanced rules seem hard at first. The same six-attribute checklist works for every problem. Just remember to look more carefully at details like relationships between parts of a figure, not just the parts themselves. As you practice more problems, you'll start to spot these tricky patterns faster.

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LOOKING AHEAD

On the real TACHS, you'll have about 30 seconds per question. Building a habit of quickly scanning all six attributes will help you work faster. Practice makes this process feel automatic over time.

SECTION 9

Practice Problems

Try these five problems on your own. Read each one carefully, identify the rule, and pick the correct answer. Check the answer explanations after you finish.

Question 1: CONCEPTUAL

Three given figures are: a shaded circle, a shaded square, and a shaded triangle. Which answer choice follows the same rule? (A) An empty hexagon. (B) A shaded pentagon. (C) A striped circle. (D) A small empty triangle.

Show answer

The correct answer is (B). The rule is that all figures are shaded. The shapes are all different, so shape doesn't matter — only shading does. Choice (B) is a shaded pentagon, which follows the "shaded" rule. Choices (A) and (D) are empty, and choice (C) is striped, not solidly shaded.

Question 2: BASIC CALCULATION

Three given figures are: a small empty triangle, a small empty square, and a small empty circle. Which answer choice follows the same rule? (A) A large empty hexagon. (B) A small shaded diamond. (C) A small empty pentagon. (D) A medium empty triangle.

Show answer

The correct answer is (C). The rule has two attributes: all figures are small AND empty. Choice (A) is large, breaking the size rule. Choice (B) is shaded, breaking the shading rule. Choice (D) is medium-sized, also breaking the size rule. Only choice (C) is both small and empty.

Question 3: INTERMEDIATE

Three given figures are: a large shaded triangle pointing up, a large shaded triangle pointing right, and a large shaded triangle pointing down. Which answer choice follows the same rule? (A) A small shaded triangle pointing left. (B) A large empty triangle pointing left. (C) A large shaded square. (D) A large shaded triangle pointing left.

Show answer

The correct answer is (D). The three figures are all large, shaded, and triangles. Orientation (the direction they point) changes across the given group, so it is NOT part of the rule. Choice (A) breaks the size rule (small). Choice (B) breaks the shading rule (empty). Choice (C) breaks the shape rule (square). Only choice (D) is large, shaded, and a triangle.

Question 4: APPLIED

Three given figures each contain a circle inside a square. In Figure 1 both are empty, in Figure 2 both are shaded, and in Figure 3 the outer square is striped and the inner circle is striped. Which answer choice follows the same rule? (A) A triangle inside a circle. (B) A square inside a square. (C) A diamond inside a hexagon with both being dotted. (D) A circle inside a square with the circle shaded and the square empty.

Show answer

The correct answer is (C). The rule is that each figure has a circle inside a square, but wait — we need to look more carefully. The key shared trait is that each figure has one shape inside another shape. However, choices (A), (B), and (C) all show shapes inside shapes. The additional rule is that the inner and outer shapes always have the same shading pattern. In (D), the shadings don't match. In (A) and (B), the relationship isn't specified. Choice (C) explicitly states both shapes are dotted (matching shading), so (C) follows the same classification rule.

Question 5: CRITICAL THINKING

Three given figures are: a pentagon with 3 dots inside, a triangle with 3 dots inside, and a hexagon with 3 dots inside. Which answer choice follows the same rule? (A) A square with 4 dots inside. (B) A circle with 3 dots inside. (C) A triangle with 3 lines inside. (D) An octagon with no dots inside.

Show answer

The correct answer is (B). At first glance, you might focus on the outer shapes, but they are all different (pentagon, triangle, hexagon), so the shape itself isn't part of the rule. The shared trait is that every figure has exactly 3 dots inside it. Choice (A) has 4 dots — wrong number. Choice (C) has lines instead of dots — wrong inner detail. Choice (D) has no dots at all. Only choice (B) has exactly 3 dots inside, which matches the classification rule. This problem teaches you that inner details can be the entire rule.

SUMMARY

Lesson Summary

Summary

Figure classification questions on the TACHS ask you to find the hidden classification rule that connects a group of three figures. To solve them, examine six key attributes: shape, size, shading, number of sides, orientation, and inner details. The rule might involve one, two, or even three attributes working together. Focus on what stays the same across all three given figures — that's your rule.

Once you identify the rule, test every answer choice against it. Eliminate choices that break any part of the rule. The correct answer will match every attribute in the rule. With practice, this process will become fast and natural. Remember: be a detective, check all the evidence, and don't rush to your answer!