Grade 2 · Geometry · MAT-02-GEO-001
Identify Triangles, Quadrilaterals, Pentagons, and Hexagons
Classify polygons by number of sides and vertices.
Learning objectives
What you should be able to do
- Classify polygons by number of sides and vertices.
- Distinguish triangles, quadrilaterals, pentagons, and hexagons from nonexamples.
- Explain why size, orientation, and color do not change polygon classification.
Prerequisite check
Make sure the foundation is ready.
Checks basic shape-attribute vocabulary.
Learn
Build the idea from meaning, not memorization.
Polygons are closed shapes made from straight segments
A polygon is a closed two-dimensional figure whose boundary is made of straight line segments. Curved boundaries or open paths do not satisfy this definition.
Count sides to classify
Triangles have3 sides, quadrilaterals4, pentagons5, and hexagons6. The number of vertices matches the number of sides for these simple polygons.
Orientation does not change identity
A triangle remains a triangle when rotated. A hexagon remains a hexagon whether it is wide, narrow, regular, or irregular, as long as it has six straight sides and is closed.
Attributes matter more than appearance
Color, size, and decorative style are non-defining attributes. Side count and closure are defining attributes.
Interactive math lab
Change it. See what stays true.
Geometry Explorer
- count sides
- rotate shape
- sort polygons
- spot nonexamples
Worked examples
Twenty different ways to see the concept work.
Closed shape3 straight sides.
triangleThree sides.
Closed shape4 straight sides.
quadrilateralFour sides.
Closed shape5 straight sides.
pentagonFive sides.
Closed shape6 straight sides.
hexagonSix sides.
Open3-segment path.
not polygonNot closed.
Circle.
not polygonCurved boundary.
Rotated triangle.
triangleOrientation irrelevant.
Long thin4-sided shape.
quadrilateralFour straight sides.
Irregular5-sided shape.
pentagonSide count decides.
Regular6-sided shape.
hexagonSix sides.
How many vertices triangle?
3Corners match sides.
Quadrilateral vertices.
4Four corners.
Pentagon vertices.
5Five corners.
Hexagon vertices.
6Six corners.
Shape has4 sides, red color.
quadrilateralColor non-defining.
Shape has5 sides, tiny size.
pentagonSize non-defining.
Shape has6 sides, one concave-looking indentation.
hexagon if simple closed six-segment boundaryRegularity not required.
Three sides but one curved.
not triangleTriangle sides must be straight segments.
Why square is quadrilateral.
It has4 straight sides and is closedQuadrilateral category is broad.
Classify by side count rather than name memory.
3 triangle,4 quadrilateral,5 pentagon,6 hexagonAttribute rule.
Practice
Guided practice with hints
01Count sides of pentagon.
Hint: Trace boundary.
Answer: 5
02Rotated4-sided shape.
Hint: Count sides.
Answer: quadrilateral
03Open5-side path.
Hint: Check closure.
Answer: not polygon
04Circle polygon?
Hint: Boundary curved.
Answer: No
05Why color irrelevant?
Hint: Doesn't change sides.
Answer: Non-defining attribute
06Square belongs to which broad class?
Hint: Count sides.
Answer: quadrilateral
Practice
Independent practice
013 sides
Answer: triangle
024 sides
Answer: quadrilateral
035 sides
Answer: pentagon
046 sides
Answer: hexagon
05Open shape polygon?
Answer: No
06Curved circle polygon?
Answer: No
07Rotating triangle changes class?
Answer: No
08Square broad class
Answer: quadrilateral
Common mistakes
Learn to catch the error, not just the answer.
Rotate mentally and count defining attributes.
Boundary must be straight segments.
A square satisfies the4-sided quadrilateral definition.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Identify polygonal signs, tiles, and designs.
- Sort shape cards by defining attributes.
Challenge problems
Can an irregular6-sided polygon be hexagon?
Yes
Why square is both square and quadrilateral?
It has specific square attributes and also meets broad4-side definition.
Can shape with5 straight segments but open gap be pentagon?
No
What changes a triangle into quadrilateral?
Adding a fourth side/vertex to create a closed4-side shape.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Polygon Sorter
Sort shapes by side count and reject non-polygons.
Practice
Mastery check
015-side closed shape
Answer: pentagon
026-side closed shape
Answer: hexagon
034-side broad class
Answer: quadrilateral
04Circle polygon?
Answer: No
05Open triangle-like path triangle?
Answer: No
06Does rotation matter?
Answer: No
07What defines classes here?
Answer: Number of straight sides/vertices and closure.
08Why square quadrilateral?
Answer: It has4 straight sides and is closed.
Terminology
Words to know
- polygon
- A closed2D figure made of straight line segments.
- vertex
- A corner where two sides meet.
- quadrilateral
- A polygon with4 sides.
- defining attribute
- A property required for a shape category.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.G.A.1
Recognize/draw shapes with specified attributes.