In this lesson:
Think about animals:
Shapes work the same way — categories nest inside each other.
A square is also a rectangle is also a parallelogram is also a quadrilateral.
The tree shows how each subcategory inherits all properties above it.
Each level adds a new property without removing old ones.
From parallelogram, the tree splits:
Both keep two pairs of parallel sides — they add a new property.
A square has every property in the hierarchy:
A square is a rectangle and a rhombus and a parallelogram.
A shape has these properties:
What is the most specific name? What else is it?
Four correct names for one shape!
Quadrilaterals use one hierarchy. Triangles use two independent systems:
Every triangle gets two labels — one from each system.
Note: "at least two" means equilateral is a special isosceles.
Every triangle fits exactly one angle category.
Some cells are impossible — can you see which ones?
An equilateral triangle has three equal angles: 60 + 60 + 60 = 180.
This mirrors the quadrilateral hierarchy: categories nest inside each other.
A triangle has sides of length 5, 5, and 8. All angles are less than 90 degrees.
Two labels, one from each system.
From now on, we classify shapes by measured properties, not by how they look.
"Close" is not enough in mathematics.
A square has: 4 sides, 2 parallel pairs, 4 right angles, 4 equal sides.
It belongs to six categories:
Trace the tree from bottom to top!
Decide if each statement is always true, sometimes true, or never true.
You can now classify shapes using properties and hierarchies.
In future lessons, you will:
Click to begin the narrated lesson
Classify two-dimensional figures in a hierarchy based on properties