Geometry

Defining & Non-Defining Attributes

What makes a shape a shape, regardless of size or orientation.

Foundational15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

What Makes a Triangle a Triangle?

A big red triangle and a tiny blue triangle look very different, but they're both still triangles. Figuring out why means separating the features that truly make a shape what it is from the features that could change without changing the shape's name at all.

Definition — Defining Attribute

A feature a shape must have to be called that shape — like a triangle needing exactly 3 straight sides. A non-defining attribute, like color or size, can change without changing what the shape is called.

For a triangle, having exactly 3 sides and 3 corners is defining — every triangle has that, and nothing with a different number of sides is a triangle. Color, size, and which way it's turned are non-defining — a triangle is still a triangle whether it's big, small, red, or blue.

Worked Example — Sorting Attributes for a Square

A square is yellow, small, and has 4 equal straight sides with 4 corners. Which attributes are defining? Having 4 equal sides and 4 corners is defining — every square needs that. Being yellow and small is non-defining — a purple, giant square is still a square.

Worked Example — Deciding If Two Shapes Are the Same Type

Shape A is a large green triangle. Shape B is a tiny orange triangle. Are they the same type of shape? Compare their defining attributes: both have exactly 3 straight sides and 3 corners. Since the defining attributes match, they're both triangles, even though their size and color are completely different.

Geometry Canvas

Point mode (click to add a point)LabelsMeasurementsSnap to grid

Construct

Tool

Objects

1.
Color
P1
P1: a free point, draggable on the plane
2.
Color
P2
P2: a free point, draggable on the plane
3.
Color
P3
P3: a free point, draggable on the plane
4.
Color
poly1
poly1: the polygon through P1, P2, P3

Measurements

poly1area = 15perimeter = 17.66

Tip

When deciding what kind of shape something is, count its sides and corners first — that's almost always the defining attribute — and ignore color and size.

Common Mistakes

Deciding two shapes are different types just because they're different colors or sizes.
Check the number of sides and corners, not the color or size, to decide whether two shapes are the same type.
Assuming a shape must be turned a certain way to count, such as not recognizing a triangle balanced on one point.
Which way a shape is turned is non-defining. A triangle is still a triangle no matter how it's rotated.

Key Takeaways

A defining attribute, like the number of sides, is required for a shape to be that type.
A non-defining attribute, like color, size, or orientation, can change without changing the shape's name.
Comparing shapes means comparing their defining attributes, not their appearance.

Summary

Defining attributes are what truly make a shape the shape it is. The next lesson uses that understanding to build brand-new shapes by combining simpler ones together.

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