Classifying 2D Shapes

🔷 Classifying 2D Shapes

Part 1 of 5 — Concept Introduction

Welcome to the world of geometry! A two-dimensional (2D) shape is a flat shape — it has only length and width, like a drawing on a piece of paper.

The most important family of 2D shapes is the polygons.

What Is a Polygon?

A polygon is a closed flat shape made of straight line segments. The word polygon comes from Greek words meaning "many angles."

To be a polygon, a shape must follow all of these rules:

• It is closed (no gaps — the sides connect all the way around).
• Every side is a straight line segment (no curves).
• The sides only meet at their endpoints (they don't cross).

So a circle is not a polygon (it's curved), and the letter "C" is not a polygon (it's open). But a triangle, a square, and a stop sign are polygons. ✅

Naming Polygons by Their Sides

We classify polygons by counting their sides. The number of sides always equals the number of angles (corners).

Polygon	Number of Sides	Number of Angles
Triangle	3	3
Quadrilateral	4	4
Pentagon	5	5
Hexagon	6	6
Octagon	8	8

Helpful memory tricks:

• A tricycle has 3 wheels → a triangle has 3 sides.
• An octopus has 8 arms → an octagon has 8 sides.
• A stop sign is an octagon — count the sides next time you see one!

Regular vs. Irregular Polygons

Polygons can also be sorted by whether their sides and angles are all equal:

• Regular polygon: all sides are the same length and all angles are equal. (Example: a stop sign, where all 8 sides match.)
• Irregular polygon: the sides are not all equal, or the angles are not all equal.

Worked example: Is a square regular or irregular?

A square has 4 equal sides and 4 equal angles (each $90°$). Because everything matches, a square is a regular polygon. ✅

A rectangle that is longer than it is wide has equal angles but unequal sides, so it is irregular.

Concept Check 🎯

Let's make sure you can spot a polygon and name it.

📐 Worked Examples: Triangles & Quadrilaterals

Part 2 of 5 — Worked Examples

Classifying Triangles

A triangle has exactly 3 sides and 3 angles, and its angles always add up to $180°$. We can classify triangles two ways.

By sides:

• Equilateral: all 3 sides equal (and all 3 angles are $60°$).
• Isosceles: exactly 2 sides equal.
• Scalene: all 3 sides different.

By angles:

• Acute: all 3 angles are less than $90°$.
• Right: one angle is exactly $90°$.
• Obtuse: one angle is greater than $90°$.

Worked example: A triangle has angles of $90°$, $45°$, and $45°$. Two of its sides are equal. Classify it by angle and by side.

• It has a $90°$ angle, so by angle it is a right triangle.
• It has 2 equal sides, so by side it is isosceles.

So it is a right isosceles triangle. ✅ (Check: $90 + 45 + 45 = 180°$.)

Classifying Quadrilaterals

A quadrilateral has exactly 4 sides and 4 angles, and its angles always add up to $360°$. Here are the most common kinds:

Quadrilateral	Key Properties
Square	4 equal sides, 4 right angles
Rectangle	opposite sides equal, 4 right angles
Parallelogram	both pairs of opposite sides parallel & equal
Rhombus	4 equal sides, opposite sides parallel
Trapezoid	exactly one pair of parallel sides
Kite	two pairs of equal sides that are next to each other

Worked example: A shape has 4 equal sides, opposite sides are parallel, but its angles are not $90°$ (it looks like a square tilted over). What is it?

• 4 equal sides + slanted (not right) angles → it is a rhombus.
• It is not a square because a square needs $90°$ angles. ✅

Your Turn 🧮

A polygon has 6 sides, and all 6 sides are equal in length with all angles equal.

1. How many sides does this polygon have? (Type a number.)

2. What is the name of a 6-sided polygon? (Type one word, all lowercase: like "hexagon".)

3. Because all of its sides and angles are equal, is it regular or irregular? (Type one word, all lowercase.)

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Read each clue carefully, then choose the best classification.

Match the Shape 🔍

Use what you know about sides and angles to complete each statement.

🌍 Application & Word Problems

Part 4 of 5 — Real-World Shapes

Shapes are everywhere in the real world! Knowing how to classify them helps you describe signs, tiles, buildings, and art.

Signs Around Town 🚸

• A yield sign is a triangle.
• A stop sign is an octagon (8 sides).
• A "Do Not Enter" sign is a circle — but remember, a circle is not a polygon because it is curved!

Floor Tiles 🧩

Imagine a kitchen floor covered in tiles. Each tile is a polygon with 4 equal sides and 4 right angles. That makes every tile a square. If the tiles were longer than they were wide (still with 4 right angles), they would be rectangles instead.

The key is always the same: count the sides, check the angles, and look for equal or parallel sides.

Word Problem Practice 🧮

A soccer ball is covered in flat patches. One type of patch is a polygon with 5 straight, equal sides.

1. How many sides does this patch have? (Type a number.)

2. What is the name of a 5-sided polygon? (Type one word, all lowercase.)

3. A stop sign has 8 sides. What is the name of an 8-sided polygon? (Type one word, all lowercase.)

Apply It 🎯

Use real-world reasoning to classify the shape.

🏆 Review & Challenge

Part 5 of 5 — Putting It All Together

You've learned how to classify 2D shapes by counting sides, checking angles, and looking for equal or parallel sides. Here's a quick summary.

Shape Cheat Sheet

Shape	Sides	Special Property
Triangle	3	Angles add to $180°$
Quadrilateral	4	Angles add to $360°$
Pentagon	5	5 sides, 5 angles
Hexagon	6	6 sides, 6 angles
Octagon	8	Like a stop sign
Square	4	4 equal sides, 4 right angles
Rectangle	4	Opposite sides equal, 4 right angles
Rhombus	4	4 equal sides, slanted angles
Trapezoid	4	Exactly 1 pair of parallel sides

Remember the big rules:

• A polygon is closed and made of straight sides.
• Regular = all sides and all angles equal; otherwise it is irregular.
• Classify triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).

Final Challenge 🎯

These questions mix everything together. Take your time!