Classifying 2D Shapes for 5th Grade: Polygons and Properties

Classifying two-dimensional (2D) shapes means grouping them by their properties: number of sides, number of angles, types of angles (right, acute, obtuse), side lengths (equal or not), and symmetry. In Grade 5, students identify polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), distinguish rectangles from squares, and use properties like “4 sides, 4 right angles, all sides equal” to identify a square.

Key prefixes: “tri-” = 3, “quad-” = 4, “penta-” = 5, “hexa-” = 6, “hepta-” = 7, “octa-” = 8. A polygon is a closed shape with straight sides. A quadrilateral has 4 sides; a rectangle has 4 right angles; a square is a rectangle with all sides equal.

DETAILED EXPLANATION

Polygon names by number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8).

Quadrilaterals: parallelogram (opposite sides parallel), rectangle (4 right angles), square (4 right angles + all sides equal), rhombus (all sides equal), trapezoid (at least one pair of parallel sides).

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Vertices = corners. A polygon with n sides has n vertices and n angles.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

A shape has 4 sides, 4 right angles, and all sides equal. What shape is it?

Solutions:

Step 1: 4 sides = quadrilateral.

Step 2: 4 right angles = rectangle (or square, since a square is a type of rectangle).

Step 3: All sides equal = square (a rectangle with all sides equal is a square).

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Step 4: The shape is a square.

Answer: A square

Example 2

How many sides does a hexagon have? How many vertices?

Solutions:

Step 1: “Hexa” means 6. A hexagon has 6 sides.

Step 2: In any polygon, the number of vertices equals the number of sides.

Step 3: A hexagon has 6 sides and 6 vertices.

Answer: 6 sides, 6 vertices

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Example 3

A shape has 5 sides and 5 angles. What is it?

Solutions:

Step 1: “Penta” means 5. A polygon with 5 sides and 5 angles is a pentagon.

Answer: A pentagon

Example 4

A quadrilateral has 4 right angles but not all sides equal. What shape could it be?

Solutions:

Step 1: 4 right angles means it could be a rectangle or a square.

Step 2: Not all sides equal rules out a square.

Step 3: The shape is a rectangle (that is not a square).

Answer: A rectangle