Basic Geometrical Ideas

Triangles and Quadrilaterals

Learning about geometric shapes is quite useful in case we are going to pave our future in fields such as engineering and architecture. What exactly is a polygon? Can a square be a polygon? You can call a polygon as the largest named group holding several geometric shapes. In this lesson, we would try to understand the importance and types of triangle and quadrilaterals which are an important part of this group.

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Introduction

A triangle is a simple closed curve or polygon which is created by three line-segments. In Euclidean geometry, any three points, specifically non-collinear, form a unique triangle and separately, a unique plane (known as two-dimensional Euclidean space).

On the other hand, in terms of Euclidean plane geometry, a polygon having four edges (or sides) together with four vertices is called a quadrilateral. At times, the term quadrangle can be used and sometimes tetragon for uniformity with pentagon (5-sided) or hexagon (6-sided).

Types of Triangle

Primarily there are three types of triangle, namely:

  • Acute Triangle: This is a triangle in which all the angles are acute.
  • Right Angled Triangle: It is a form of a triangle wherein one particular angle is a right angle.
  • Obtuse Triangle: Triangle in which one of the angles stays obtuse is called as an obtuse triangle.

Further, triangles can be segregated depending on the number of congruent sides. Therefore, you can count on two different ways to classify the types of triangle:

  • Scalene, meaning that every side length in a triangle tends to be different.
  • Equilateral means that every side length in a triangle is similar.
  • Isosceles triangle means, at least two of the triangle side lengths are similar.

Quadrilateral Types & Properties

We can define quadrilateral as a Polygon that has four sides. There are more properties associated to a quadrilateral as compared to a triangle. In a quadrilateral, one amazing aspect is that it can have parallel opposite sides.

Hence, if every side holds a parallel opposite side, this shape is termed as a parallelogram. It is important to note that, rectangles, rhombuses (rhombi) and squares are all parallelograms since their opposite sides are parallel (always). Furthermore, a rhombus holds four sides of equal length.

Quadrilaterals that have a single pair of parallel sides are called trapezoids. According to some math books, a trapezoid holds at least one pair of parallel sides. It means that this would form a parallelogram if there are two sets of parallel sides, making it a special kind of a trapezoid.  Moreover, as per other math books, trapezoids possess only a single pair of parallel sides; this is strictly followed in high school level mathematics.

Geometric Properties of Quadrilaterals

a) Square

  • Opposite sides are parallel, with all sides being equal
  • Each of the angles is 90°
  • A square has four lines of symmetry
  • The order of rotational symmetry is 4
  • The diagonals bisect each other at 90° or right angles

b) Rectangle

  • The opposite sides are parallel and equal
  • All the angles in a rectangle are 90°
  • Lines of symmetry are two
  • Rectangle has a rotational symmetry of 2

c) Parallelogram

  • The opposite sides are parallel and equal
  • Parallelogram has equal opposite angles
  • There are no symmetry lines
  • Rotational symmetry order is 2

d) Kite

  • A kite has a single line of symmetry
  • The diagonals intersect at 90° or right angles

Questions For You

Q1. What is a triangle with one angle greater than 90° called?

Ans: Obtuse Triangle

Q2. A triangle with three equal sides is called as?

Ans: Equilateral triangle

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