write the definition and properties of all types of triangle and quadrilateral.
Answers
Answer:
Triangles are shapes with three sides. There are different names for the types of triangles. A triangle's type depends on the length of its sides and the size of its angles (corners). There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
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