Grade 2 geometry lesson
Corners and Sides of Plane Figures
Plane figures are flat shapes. Some have straight sides and corners, while circles and ovals have curved boundaries and no corners.
What are plane figures?
A plane figure is a flat, two-dimensional shape. It can be drawn on paper, a board, or a screen.
Plane figures can have straight sides, curved boundaries, corners, or a mix of these features.
A plane figure made only from straight sides is called a polygon. Triangles, rectangles, pentagons, and hexagons are polygons.
Corners and sides chart
Use this chart to compare common plane figures. The chart shows the shape name, the number of straight sides, and the number of corners.
A corner is where two straight sides meet. A side is a straight line segment. Curved shapes such as circles and ovals do not have straight sides or corners.
Corners and sides of a circle
A circle is a round plane figure. It has a curved boundary all the way around.
A circle has 0 straight sides and 0 corners because no two straight sides meet.
Corners and sides of an oval
An oval is a stretched round plane figure. It is curved like a circle, but it is longer in one direction.
An oval has 0 straight sides and 0 corners.
Corners and sides of a triangle
A triangle is a plane figure with 3 straight sides.
A triangle has 3 corners. Each corner is made where two sides meet.
Corners and sides of a square
A square has 4 straight sides. All 4 sides are the same length.
A square has 4 corners. Its corners are square corners, or right angles.
Corners and sides of a rectangle
A rectangle has 4 straight sides. Opposite sides are the same length.
A rectangle has 4 corners. Like a square, each corner is a right angle.
Corners and sides of a rhombus
A rhombus has 4 straight sides, and all 4 sides are the same length.
A rhombus has 4 corners. A diamond shape is a common way to draw a rhombus.
Corners and sides of a parallelogram
A parallelogram has 4 straight sides. Opposite sides are parallel.
A parallelogram has 4 corners. It can look like a rectangle that has been pushed sideways.
Corners and sides of a trapezoid
A trapezoid has 4 straight sides. In many classrooms, a trapezoid is introduced as a shape with one pair of parallel sides.
A trapezoid has 4 corners.
Corners and sides of a pentagon
A pentagon has 5 straight sides.
A pentagon has 5 corners. The word begins with penta, which helps remind students of 5.
Corners and sides of a hexagon
A hexagon has 6 straight sides.
A hexagon has 6 corners. A honeycomb cell is often drawn as a hexagon.
Corners and sides of a heptagon
A heptagon has 7 straight sides.
A heptagon has 7 corners.
Corners and sides of an octagon
An octagon has 8 straight sides.
An octagon has 8 corners. A stop sign is a common real-world octagon.
Corners and sides of a nonagon
A nonagon has 9 straight sides.
A nonagon has 9 corners.
Corners and sides of a decagon
A decagon has 10 straight sides.
A decagon has 10 corners.
The polygon rule
For a polygon, the number of straight sides and the number of corners are the same.
A 5-sided polygon has 5 corners. A 9-sided polygon has 9 corners. A 12-sided polygon has 12 corners.
This rule works because every straight side ends at a corner, and the corners connect the sides around the shape.
How to count corners and sides
Step 1: Start at one corner or one side and mark it with your finger.
Step 2: Move around the outside of the shape one side at a time.
Step 3: Count each straight side once.
Step 4: Count each place where two straight sides meet.
Step 5: Check whether the shape is curved. Curved shapes do not use the polygon rule.
Common mistakes
Do not count a curved boundary as a straight side.
Do not count the same corner twice when you return to the starting point.
Do not think every 4-sided shape is a square. Squares, rectangles, rhombuses, parallelograms, and trapezoids all have 4 sides and 4 corners, but their side lengths and angles can be different.
Quick practice
1. How many sides does a triangle have? Answer: 3.
2. How many corners does a rectangle have? Answer: 4.
3. How many straight sides does a circle have? Answer: 0.
4. How many corners does a hexagon have? Answer: 6.
5. What shape has 8 sides and 8 corners? Answer: an octagon.