ISEE LOWER LEVEL • MATHEMATICS ACHIEVEMENT

Identify a polygon based on its properties.

Learn how to name shapes by counting their sides and angles like a geometry detective!

Where Did Polygon Names Come From?

People have been studying shapes for thousands of years! Long ago, in ancient Greece and Egypt, builders needed to understand shapes to create amazing buildings and pyramids. The word polygon comes from two Greek words: "poly" means many and "gon" means angles. So polygon literally means "many angles"!

2600 BC
Egyptian Pyramids
Ancient Egyptians used triangles and squares to build the Great Pyramids. Each face of a pyramid is a triangle!
300 BC
Euclid's Geometry Book
A Greek mathematician named Euclid wrote a famous book describing the rules of shapes. He gave names to many polygons we still use today.
200 BC
Archimedes Studies Polygons
Archimedes discovered special polygons with equal sides and angles. He even used polygons to estimate the value of pi!
TODAY
Polygons Are Everywhere
We see polygons in stop signs (octagons), soccer balls (pentagons and hexagons), and even honeycombs (hexagons)!

On the ISEE test, you will see questions that ask you to name a shape. The key is knowing how to count sides and angles and match them to the right polygon name. Let's learn how!

What Makes a Shape a Polygon?

Before we name polygons, we need to know what counts as one! A polygon is a flat, closed shape made of straight lines. That's it! But every part of that definition matters.

1

Closed Shape

All the sides must connect. No gaps! Imagine drawing a shape without lifting your pencil and ending where you started.
2

Straight Sides Only

Every side must be a straight line. Circles and ovals are NOT polygons because they have curved edges.
3

Flat (2D) Shape

Polygons are flat, like a drawing on paper. A box or a ball is 3D — those are not polygons.
4

At Least 3 Sides

You need at least 3 straight sides to make a closed shape. The simplest polygon is the triangle!
5

Name = Number of Sides

Each polygon is named by how many sides it has. Count the sides and you know the name. It's like a secret code!
KEY TAKEAWAY
Think of a polygon like a fence around a yard. The fence must go all the way around (closed), it must be made of straight boards (straight sides), and you can count the boards to find out the shape's name!

See the Polygons!

Let's look at the most common polygons you'll see on the ISEE. Notice how each one has a different number of sides. The number of sides always equals the number of angles (corners)!

Each polygon above is labeled with its name and number of sides. The colored dots show the corners, called vertices. Notice that a triangle has 3 dots, a square has 4 dots, and so on. The number of vertices always matches the number of sides!

Here's a handy trick: count the sides, then match the number to the name. A shape with 5 sides? That's a pentagon. A shape with 8 sides? That's an octagon — just like a stop sign!

The Number Rules for Polygons

There are some cool number rules that help you check your answers. Let's learn them!

SIDES AND ANGLES RULE
Number of sides = Number of angles
Every polygon has the same number of sides and angles. A triangle has 3 sides AND 3 angles. A hexagon has 6 sides AND 6 angles. This is always true!
VERTICES RULE
Number of vertices = Number of sides
A vertex (plural: vertices) is a corner where two sides meet. The number of vertices also equals the number of sides.
REGULAR POLYGON RULE
Regular polygon = All sides equal + All angles equal
A regular polygon has all sides the same length and all angles the same size. A square is a regular polygon. A rectangle is NOT regular because its sides are not all the same length.
💡 ISEE Test Tip!
If a question asks "Which shape has exactly 4 sides and 4 right angles?", don't just pick the first 4-sided shape you see. A rhombus has 4 equal sides but does NOT always have right angles. Read every detail carefully!

The Polygon Name Chart

Here is a chart of the polygon names you need to know for the ISEE. Study this table — it's your cheat sheet!

Polygon names from 3 to 10 sides
Number of SidesPolygon NameReal-Life Example
3TriangleSlice of pizza, yield sign
4QuadrilateralBook, window, TV screen
5PentagonThe Pentagon building, some star shapes
6HexagonHoneycomb cell, some nuts and bolts
7HeptagonSome coins, some windows
8OctagonStop sign
9NonagonRare, but sometimes in tile patterns
10DecagonSome star designs
The left side shows real polygons — they are closed and have straight sides. The right side shows shapes that are NOT polygons because they are either curved (like circles) or open (the sides don't connect).
🧠 Memory Helper!
Use the prefix to remember the number! "Tri" means 3 (like tricycle). "Quad" means 4. "Pent" means 5 (think Pentagon building). "Hex" means 6 (think hexagonal honeycomb). "Oct" means 8 (think octopus with 8 arms)!

Let's Solve One Together!

Here's the kind of question you'll see on the ISEE. Let's walk through it step by step.

A shape has 6 straight sides, 6 angles, and all sides are the same length. What is the name of this shape?
1
Step 1 — Check: Is It a Polygon?The question says the shape has "straight sides." It has 6 of them and 6 angles, so it must be closed. Straight sides + closed shape = polygon!
Yes, it is a polygon ✓
2
Step 2 — Count the SidesThe question tells us there are 6 sides. This is the most important clue! The number of sides gives us the name.
6 sides
3
Step 3 — Match the Number to the NameLook at our chart: 3 = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon. A shape with 6 sides is a hexagon!
Hexagon
4
Step 4 — Check for Bonus DetailsThe question also says "all sides are the same length." That means it is a REGULAR hexagon. But the basic name is still hexagon.
Answer: Regular hexagon
🎯 STRATEGY REMINDER
When you see a polygon question, follow these steps every time: (1) Check if it's a polygon (closed + straight sides), (2) count the sides, (3) match the number to the name. This 3-step process works for every question!

Special Quadrilaterals — The 4-Sided Family

The ISEE loves to ask about 4-sided shapes. All 4-sided polygons are called quadrilaterals. But there are special types of quadrilaterals with their own names. Let's compare them!

Types of quadrilaterals and their properties
ShapeSpecial PropertiesRight Angles?
Square4 equal sides, 4 equal anglesYes — all 4 are right angles
RectangleOpposite sides equal, 4 equal anglesYes — all 4 are right angles
Rhombus4 equal sides, opposite angles equalNot always
ParallelogramOpposite sides equal and parallelNot always
TrapezoidExactly 1 pair of parallel sidesNot always
KEY TAKEAWAY
Think of quadrilaterals like a family. "Quadrilateral" is like saying "pet." A square is a specific type — like saying "golden retriever." Every square is a rectangle, but not every rectangle is a square. It's like how every golden retriever is a dog, but not every dog is a golden retriever!

Regular vs. Irregular Polygons

When you move on to harder math classes, you'll learn more about regular and irregular polygons. For now, here's the basic idea.

Regular vs. irregular polygons
FeatureRegular PolygonIrregular Polygon
SidesAll sides are the same lengthSides can be different lengths
AnglesAll angles are the same sizeAngles can be different sizes
ExampleA perfect square, equilateral triangleA lopsided rectangle, a scalene triangle
Looks like...Perfectly balanced and evenMight look stretched or tilted

The great news is that on the ISEE, you mainly need to count sides to name the polygon. Whether a hexagon is regular or irregular, it still has 6 sides and is still called a hexagon. Keep it simple and count!

Practice Problems

Time to practice! Remember: count the sides and match to the name. Try each question before reading the answer. You've got this!

1
Which of the following is a polygon?
2
A shape has exactly 5 sides and 5 angles. What is it called?
3
A stop sign has 8 equal sides and 8 equal angles. What type of polygon is it?
4
Maria draws a shape with 4 sides. Two sides are parallel, but the other two sides are not parallel. Which shape did Maria most likely draw?
5
A polygon has 4 sides. All 4 sides are the same length, but the angles are NOT all the same. Which shape is it?

Let's Review What You Learned!

A polygon is a closed, flat shape with straight sides. You name a polygon by counting its sides: 3 sides = triangle, 4 sides = quadrilateral, 5 sides = pentagon, 6 sides = hexagon, and 8 sides = octagon. The number of sides always equals the number of angles and vertices (corners).

For 4-sided shapes, remember the special names: a square has 4 equal sides and 4 right angles, a rectangle has opposite sides equal and 4 right angles, a rhombus has 4 equal sides but angles may differ, and a trapezoid has exactly one pair of parallel sides. A regular polygon has all sides and all angles equal. On the ISEE, always count the sides first, then look at other properties to pick the best answer. You've got this!

Varsity Tutors • ISEE Lower Level • Identify a polygon based on its properties.