Classifying Shapes

🔺 Classifying Shapes

Part 1 of 5 — Sides, Vertices & Angles

Topics in This Part

🔑 Key Idea: A polygon is a closed, flat shape made of straight sides. To classify any shape, we first learn to count its parts — its sides, its vertices (corners), and its angles.

What Makes a Polygon?

A shape is a polygon only if it follows three rules:

1. It is closed — the sides connect all the way around with no gaps.
2. Every side is a straight line segment (no curves).
3. The sides do not cross over each other.

💡 A circle is a shape, but it is not a polygon, because "poly-gon" means "many straight sides."

Concept Check 🎯

The Parts of a Polygon

Every polygon has three things we can count:

• Sides — the straight line segments.
• Vertices — the corners where two sides meet. (One corner is a "vertex"; many corners are "vertices.")
• Angles — the amount of "opening" at each corner.

🔑 Super-Helpful Rule: In any polygon, the number of sides, the number of vertices, and the number of angles are all the same! A shape with 5 sides has 5 vertices and 5 angles.

Count the Parts 🧮

Use the rule "sides = vertices = angles" to fill in the blanks.

1) A hexagon has 6 sides. How many vertices does it have? 2) A shape has 8 angles. How many sides does it have? 3) A triangle has how many vertices?

Naming Shapes by Their Sides

Polygons are named by how many sides they have:

💡 The word ending "-gon" comes from a word meaning "angle" — so a hexagon literally means "six angles," which is also six sides.

You can now count and name shapes. In Part 2 we look closely at the most important family of all: triangles.

Name That Polygon 🔽

Pick the correct name for a polygon with the given number of sides.

🔺 Classifying Shapes

Part 2 of 5 — Classifying Triangles

🔑 The Idea: Every triangle has 3 sides and 3 angles. We can sort triangles two different ways — by their sides or by their angles.

Sorting Triangles by Their Sides

Look at how many sides have the same length:

💡 Memory trick: Equilateral means "equal sides" — all three match. The tick marks (small lines) on a side tell you which sides are equal.

Sorting Triangles by Their Angles

Now look at the biggest angle in the triangle. (Remember: a right angle is a square corner, exactly 90°.)

⚠️ Watch out: A triangle can only ever have one right angle or one obtuse angle — never two. The other corners must be acute.

Concept Check 🎯

Sort by Angles 🔽

Choose the correct triangle name for each clue about its angles.

Count the Equal Sides 🧮

Match each triangle to the number of equal sides it has.

1) How many equal sides does an equilateral triangle have? 2) How many equal sides does an isosceles triangle have? 3) How many equal sides does a scalene triangle have?

🔺 Classifying Shapes

Part 3 of 5 — Classifying Quadrilaterals

🔑 The Idea: A quadrilateral is any polygon with 4 sides. But not all 4-sided shapes are the same! We sort them by their parallel sides, equal sides, and right angles.

First, a Key Word: Parallel

Parallel sides are two sides that run in the same direction and never cross, like the two rails of a train track. They stay the same distance apart forever.

💡 Picture it: The top and bottom edges of this page are parallel. The left and right edges are parallel too.

Quadrilaterals are sorted by how many pairs of parallel sides they have:

• 0 pairs — a general quadrilateral.
• 1 pair — a trapezoid.
• 2 pairs — a parallelogram (and its special versions).

The Quadrilateral Family

🔑 A square is special: It is a rectangle (4 right angles) and a rhombus (4 equal sides) at the same time. A square is the "best of both."

Concept Check 🎯

Why a Square Counts as Many Shapes

Because a square has everything, it belongs to several groups at once:

$\text{Square} = \text{rectangle} + \text{rhombus}$

• It has 4 right angles → so it is a rectangle. ✅
• It has 4 equal sides → so it is a rhombus. ✅
• It has 2 pairs of parallel sides → so it is a parallelogram. ✅
• It has 4 sides → so it is a quadrilateral. ✅

⚠️ But be careful — it does NOT go backwards! Every square is a rectangle, but not every rectangle is a square. A rectangle only becomes a square when all 4 sides are equal.

Name That Quadrilateral 🔽

Pick the best name for each shape from its description.

Count the Parallel Pairs 🧮

Write how many pairs of parallel sides each quadrilateral has.

1) How many pairs of parallel sides does a trapezoid have? 2) How many pairs of parallel sides does a parallelogram have? 3) How many pairs of parallel sides does a square have?

🔺 Classifying Shapes

Part 4 of 5 — Lines, Angles & Symmetry

🔑 The Idea: Beyond counting sides, we classify shapes using their lines (parallel and perpendicular), their angles (right, acute, obtuse), and their lines of symmetry.

Parallel vs. Perpendicular Lines

These two words describe how lines relate to each other:

💡 Spot the difference: Parallel lines look like = (they run alongside each other). Perpendicular lines look like + or L (they meet at a square corner).

⚠️ Don't mix these up! "Perpendicular" always makes a right angle where the lines meet.

Concept Check 🎯

Lines of Symmetry

A line of symmetry is a line you could fold a shape along so that both halves match up perfectly — like folding a paper heart in half.

A shape can have zero, one, or many lines of symmetry.

💡 The pattern: A regular polygon (all sides and angles equal) has the same number of lines of symmetry as it has sides. A regular hexagon (6 sides) has 6 lines of symmetry.

Count the Lines of Symmetry 🧮

Use the table above to answer.

1) How many lines of symmetry does a square have? 2) How many lines of symmetry does an equilateral triangle have? 3) A regular pentagon has 5 sides. How many lines of symmetry does it have?

Symmetry Check 🔽

Choose how many lines of symmetry each shape has.

🔺 Classifying Shapes

Part 5 of 5 — Mixed Practice & Mastery Check

You can now (1) count sides, vertices, and angles, (2) classify triangles by sides and angles, (3) name quadrilaterals, and (4) find right angles, parallel lines, and lines of symmetry. Let's put it all together!

Quick Reference

🔑 Remember: Sides = vertices = angles in every polygon, and a regular shape has as many lines of symmetry as it has sides.

Mixed Practice 🎯

Counting Review 🧮

1) How many sides does an octagon have? 2) How many lines of symmetry does a square have? 3) How many pairs of parallel sides does a trapezoid have?

Exit Quiz ✅

Answer all three to finish the lesson.