Select the answer choice that follows the same classification rule

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

Lesson Summary