So What Does "Polygon ABC" Even Mean?
If you've landed here, chances are you ran into a geometry question that looks something like this: which of the following terms does not describe polygon ABC?* And the answer choices are usually some mix of — regular, equilateral, convex, equiangular, simple, maybe even cyclic or quadrilateral. In real terms, on the surface, the question feels straightforward. In practice, it's one of those things that trips up students because the wording is sneakier than it looks.
Let me walk you through it the way I'd explain it to a friend sitting next to me with a worksheet in front of them. Which means the trick isn't really about the shape. It's about understanding what each of those geometry terms actually* requires — and which ones a polygon can be without being the other.
What the Question Is Really Asking
When a test question asks "which term does not describe polygon ABC," it's not asking you to identify a shape. It's asking you to spot the term whose definition doesn't match what the diagram shows. So the answer depends entirely on what's drawn Surprisingly effective..
Most of the time, the polygon in question is shown with specific markings — little tick marks on sides showing they're equal, or arc marks on angles showing they're equal. Sometimes the shape looks like a regular figure, but only some of those properties are guaranteed Nothing fancy..
In plain terms, if the picture shows all sides equal but the angles clearly aren't, then "regular" and "equiangular" don't describe it — even though "equilateral" does. You have to read the diagram like a detective.
Why This Question Type Is Everywhere
This style of question shows up in middle school math, high school geometry, and even some standardized tests. And honestly? That said, it's popular because it tests more than just vocabulary. It tests whether you can connect a picture* to a definition*. That's a different skill than just memorizing terms.
A lot of students get it wrong because they assume a "nice-looking" shape on the page is regular. But unless every side is marked equal and every angle is marked equal, you can't call it regular. That's the trap.
The Common Answer Choices (And What They Mean)
Here's the thing — most versions of this question rotate around the same handful of terms. So let's break each one down properly. If you understand these, you can answer almost any version of the question.
Regular
A regular polygon has two things going on: all sides equal length, and all interior angles equal in measure. Both. Not just one. If either condition is missing, it's not regular — even if the shape looks like it should be Which is the point..
Equilateral
Equilateral just means "equal sides.Day to day, a rhombus is equilateral (all four sides equal) but it isn't regular unless the angles also happen to be equal. " It says nothing about the angles. So this is often the correct* answer to "which does NOT describe" — when the figure clearly has unequal angles Not complicated — just consistent..
Equiangular
Equiangular means "equal angles.But " Again, this says nothing about side lengths. A rectangle is equiangular (all 90°) but it isn't regular unless all sides are also equal — making it a square. So if the diagram shows equal angles but different side lengths, "equiangular" still describes it Most people skip this — try not to..
Convex
A convex polygon is one where all interior angles are less than 180° and no vertices "cave in" toward the interior. The entire shape bulges outward. Most textbook polygons are convex by default. If the figure looks like a normal pentagon, hexagon, or quadrilateral that doesn't fold inward, it's convex.
Simple
A simple polygon is one whose sides don't cross each other. No self-intersections, no bowtie shapes. Most standard shapes you see in geometry class are simple polygons. This one usually isn't the answer unless the diagram is doing something weird Small thing, real impact..
Concave
Concave is the opposite of convex — at least one interior angle is greater than 180°, meaning the shape has a "dent" or "notch" pointing inward. Think about it: if the figure has a star-like inward point, it's concave. This term is the one that doesn't* describe the polygon when everything else points to a convex shape The details matter here. Turns out it matters..
Cyclic
This one shows up more in advanced geometry. Also, a cyclic polygon is one where all vertices lie on a single circle. Every triangle is technically cyclic, but not every quadrilateral or pentagon is. If the diagram doesn't show a circumscribed circle, you can't assume this.
The official docs gloss over this. That's a mistake That's the part that actually makes a difference..
Quadrilateral, Pentagon, Hexagon
These just describe the number of sides. That's why if the figure clearly has five sides, "quadrilateral" doesn't describe it. Quadrilateral = 4 sides, pentagon = 5, hexagon = 6. Simple as that.
The Strategy for Picking the Right Answer
Here's what most guides get wrong — they tell you to "just memorize the definitions." That's not enough. The real strategy is two-part:
Step 1: Look at the diagram and list every property you can actually see. Equal sides marked? Equal angles marked? Any sides that look different lengths? Any vertices that dip inward?
Step 2: For each answer choice, ask: does the diagram support this term? If even one required property is missing, that term doesn't describe the polygon Worth keeping that in mind..
The answer is almost always the term whose required condition is the one thing* the diagram doesn't show. If all sides are equal but the angles clearly aren't, the answer is "regular" or "equiangular" — whichever is in the list. If all angles are equal but the sides aren't, then "regular" is the answer but "equiangular" still works.
Common Mistakes Students Make
This is where things really go sideways.
Assuming the shape is regular because it looks symmetrical. Drawings lie. Unless the tick marks are on the sides, don't assume anything Easy to understand, harder to ignore..
Confusing equilateral with regular. They are not the same word. Equilateral = equal sides. Regular = equal sides AND equal angles. A shape can be one without being the other Took long enough..
Ignoring concave vs. convex. A shape with even one inward-pointing angle is concave, full stop. The rest of the angles being less than 180° doesn't change that.
Overthinking it. Sometimes the answer really is just "quadrilateral" because the shape clearly has five sides. Don't reach for a fancy explanation when the simple one works Practical, not theoretical..
Forgetting that "simple" is usually a given. If no sides cross, it's simple. Most textbook diagrams are simple polygons, so this is rarely the right answer Small thing, real impact..
Quick Cheat Sheet for Test Day
If you want a fast mental model, here it is:
- Equal sides + equal angles = regular
- Equal sides only = equilateral (but not regular)
- Equal angles only = equiangular (but not regular)
- All angles under 180° = convex
- At least one angle over 180° = concave
- Sides don't cross = simple
- All vertices touch one circle = cyclic
When the question asks which term does not describe the polygon, you're hunting for the term whose condition the diagram fails to meet. That's it And that's really what it comes down to..
FAQ
What does "polygon ABC" mean?
It's just a way to name a specific polygon in a diagram. ) label the vertices. The letters A, B, C (and D, E, etc.The polygon is named by listing its vertices in order.
Is a square regular?
Yes. A square has four equal sides and four equal angles (all 90°), which meets both requirements for a regular polygon.
Is a rectangle regular?
No. A rectangle is equiangular (all angles equal) but its sides aren't all equal — only opposite sides are. So it fails the "regular" test.
Is a rhombus regular?
Not necessarily. A rhombus is equilateral (all four sides equal), but unless the angles are also all equal — which would make it a square — it's not regular.
Can a polygon be both equilateral and equiangular but not regular?
No. If a polygon is both equilateral and equiangular, by definition it's regular. Those two conditions together are what "regular" means.
At the end of the day, "which of these terms does not describe polygon ABC" isn't really a hard question once you slow down and actually look at the diagram. Now, the terms sound similar, and that's intentional — the test wants you to mix them up. But each one has a precise definition, and the diagram either supports it or it doesn't Small thing, real impact..
drawn, and pick the term that doesn't fit. The rest is just vocabulary.
Final Thought
Geometry vocabulary problems aren't testing whether you can solve a complex proof or compute some obscure value. That said, they're testing whether you can pay attention to what's actually in front of you. The terms are defined precisely, the diagrams are drawn deliberately, and the answer is almost always sitting right there in the markings or the lack of them That's the whole idea..
When you see "which of these does not describe polygon ABC," your job is to do exactly four things:
- Look at the diagram carefully. Note the tick marks on sides and the arc marks on angles. These are the test-makers telling you what's equal.
- Check each term against the diagram. Run through equilateral, equiangular, regular, convex, concave, simple, cyclic — whatever the options are — and see which conditions hold.
- Identify the odd one out. The term whose condition isn't met is your answer.
- Move on. Don't second-guess yourself into picking something that does technically apply.
The biggest trap on these questions is overcomplicating things. Students see a pentagon and start wondering about interior angle sums, or they see a shape that looks* weird and assume it must be concave. But the diagram is the source of truth, not your intuition about what a shape "should" look like.
A few more things worth keeping in mind for test day:
- Trust the tick marks, not your eyes. If two sides have matching tick marks, treat them as equal even if they don't look it. Diagrams aren't drawn to scale.
- Convex is the default assumption. Unless you can clearly see a vertex that bends inward, assume the polygon is convex.
- "Regular" is a strong claim. A polygon has to satisfy two conditions to be regular. If even one fails, regular is out.
- Concave is the most commonly missed. Students forget to check every single vertex. One inward bend is all it takes.
The vocabulary of polygons is finite, and the definitions don't change. Once you've internalized what each term means and what the diagram needs to show for that term to apply, these questions become almost mechanical. You're not solving a puzzle — you're running through a checklist The details matter here..
So the next time you face one of these problems, take a breath, look at the diagram, and methodically work through the options. The answer will be the term that doesn't match what you see. Nothing more, nothing less Not complicated — just consistent. Worth knowing..
And if you ever forget the difference between equilateral and regular, or convex and concave, just remember: geometry rewards precision. The test-makers chose these words carefully because they mean different things. Your job is to respect that difference and let the diagram guide you to the right answer.
