TutorialKart.comGeometric shapes are figures defined by points, lines, curves, angles, and surfaces. Two-dimensional geometric shapes have length and width but no thickness. Common examples include triangles, squares, rectangles, circles, and other polygons.
This guide explains the names, defining properties, and basic measurements of commonly used 2D geometric shapes.
Common 2D Geometric Shapes and Their Properties
Two-dimensional shapes can be grouped into polygons and curved shapes. A polygon is a closed shape made entirely from straight line segments. Triangles and quadrilaterals are polygons, while a circle has a curved boundary and is not a polygon.
Straight Line and Line Segment
A straight line does not bend and extends infinitely in both directions. Because a complete line has no endpoints, its length cannot be measured.
A line segment is a part of a line with two endpoints. Its length is fixed and can be measured. The following figure depicts a straight line segment.
Imagine extending the line segment indefinitely beyond both endpoints. The resulting figure represents a straight line.
Triangle: A Three-Sided Polygon
A triangle is a closed geometric shape formed by joining three non-collinear points with three line segments. The meeting points of the sides are called vertices.
Properties of a Triangle
- A triangle has three sides, three vertices, and three interior angles.
- The sum of its interior angles is 180 degrees.
- The perimeter is the sum of the lengths of its three sides.
- The area can be calculated as one-half of the product of its base and perpendicular height.
Triangles may be classified by their sides as equilateral, isosceles, or scalene. They may also be classified by their angles as acute, right, or obtuse triangles.
Quadrilateral: A Four-Sided Polygon
A quadrilateral is a closed polygon with four straight sides and four vertices. Squares, rectangles, rhombuses, parallelograms, and trapezoids are special types of quadrilaterals.
Properties Shared by Quadrilaterals
- A quadrilateral has four sides, four vertices, and four interior angles.
- It has two diagonals joining opposite vertices.
- The sum of its interior angles is 360 degrees.
- Its perimeter is the sum of the lengths of all four sides.
Special Types of Quadrilaterals
Special quadrilaterals are identified by relationships among their side lengths, angles, diagonals, and parallel sides.
Square
A square is a quadrilateral with four equal sides and four right angles.
Properties of a Square
- All four sides are equal in length.
- Each interior angle measures 90 degrees.
- Opposite sides are parallel.
- The diagonals are equal in length.
- The diagonals bisect each other at right angles.
- Each diagonal bisects a pair of opposite angles.
For a square with side length s, the perimeter is 4s and the area is s2.
Learn more about Square.
Rectangle
A rectangle is a quadrilateral with four right angles. Its opposite sides have equal lengths.
Properties of a Rectangle
- Opposite sides are equal in length and parallel.
- Each interior angle measures 90 degrees.
- The diagonals are equal in length.
- The diagonals bisect each other.
For a rectangle with length l and width w, the perimeter is 2(l + w) and the area is l × w.
Learn more about Rectangle.
Rhombus
A rhombus is a quadrilateral whose four sides have equal lengths. Unlike a square, its angles do not have to be right angles.
Properties of a Rhombus
- All four sides are equal in length.
- Opposite sides are parallel.
- Opposite angles are equal.
- Adjacent interior angles add up to 180 degrees.
- The diagonals bisect each other at right angles.
- The diagonals are generally unequal, except when the rhombus is a square.
If the perpendicular diagonals have lengths d1 and d2, the area of the rhombus is one-half of d1 × d2.
Learn more about Rhombus.
Parallelogram
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
Properties of a Parallelogram
- Opposite sides are parallel and equal in length.
- Opposite angles are equal.
- Adjacent interior angles add up to 180 degrees.
- The diagonals bisect each other.
- The diagonals are not necessarily equal or perpendicular.
The area of a parallelogram is its base multiplied by its perpendicular height.
Learn more about Parallelogram.
Trapezoid
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are commonly called bases, and the perpendicular distance between them is the height.
Properties of a Trapezoid
- It has at least one pair of opposite sides that are parallel.
- The parallel sides may have different lengths.
- The non-parallel sides are called legs.
- The two interior angles along the same leg add up to 180 degrees.
If the parallel sides have lengths a and b, and the perpendicular height is h, the area is one-half of (a + b) × h.
Learn more about Trapezoid.
Circle and Its Main Parts
A circle is a closed curved shape consisting of all points in a plane that are the same distance from a fixed point called the center. The boundary of a circle is called its circumference.
- Radius: A line segment from the center to a point on the circle.
- Diameter: A line segment passing through the center with endpoints on the circle. Its length is twice the radius.
- Chord: A line segment joining any two points on the circle.
- Arc: A portion of the circumference.
- Sector: A region bounded by two radii and an arc.
For a circle with radius r, the circumference is 2πr and the area is πr2.
Learn more about Circle.
Comparison of Common Geometric Shapes
| Shape | Number of sides | Number of vertices | Key identifying property |
|---|---|---|---|
| Triangle | 3 | 3 | Interior angles total 180 degrees |
| Quadrilateral | 4 | 4 | Interior angles total 360 degrees |
| Square | 4 | 4 | Four equal sides and four right angles |
| Rectangle | 4 | 4 | Opposite sides equal and four right angles |
| Rhombus | 4 | 4 | Four equal sides |
| Parallelogram | 4 | 4 | Two pairs of parallel opposite sides |
| Trapezoid | 4 | 4 | At least one pair of parallel sides |
| Circle | 0 | 0 | Every boundary point is equally distant from the center |
Perimeter and Area of Basic Geometric Shapes
Perimeter measures the total distance around a closed shape. Area measures the amount of flat surface enclosed by the shape.
| Shape | Perimeter or circumference | Area |
|---|---|---|
| Triangle | a + b + c | ½ × base × height |
| Square | 4s | s2 |
| Rectangle | 2(l + w) | l × w |
| Parallelogram | 2(a + b) | base × perpendicular height |
| Rhombus | 4s | ½ × d1 × d2 |
| Trapezoid | Sum of all four sides | ½ × (sum of parallel sides) × height |
| Circle | 2πr | πr2 |
Frequently Asked Questions About Geometric Shapes
What is the difference between a line and a line segment?
A line extends infinitely in both directions and has no endpoints. A line segment has two endpoints and a measurable length.
Is a circle a polygon?
No. A polygon is formed from a finite number of straight line segments, while a circle has one continuous curved boundary.
Is every square also a rectangle?
Yes. A rectangle is any quadrilateral with four right angles. A square satisfies this condition and also has four equal sides. However, not every rectangle is a square because a rectangle does not require all four sides to be equal.
What is the difference between a rhombus and a square?
Both shapes have four equal sides. A square must have four right angles and equal diagonals, while a general rhombus may have non-right angles and diagonals of different lengths.
How can a geometric shape be identified?
Check whether the shape is open or closed, whether its boundary is straight or curved, the number of sides and vertices, the sizes of its angles, and whether any sides are equal or parallel.