Equilateral
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.
Source: https://en.wikipedia.org/wiki/Equilateral_triangle
Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (sides) and four vertices (corners). Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided) and hexagon (6-sided), or 4-gon for consistency with k-gons for arbitrary values of k.
Source: https://en.wikipedia.org/wiki/Quadrilateral
What a Square is:
A square is a quadrilateral, which refers it to having 4 equal sides and 4 equal angles(90-degree angles also known as 4 90-degree angles).
What a Rectangle is:
A rectangle is a quadrilateral with 4 right angles(4 90-degree angles). It can also be known as an equiangular quadrilateral because all the angles are equal. It can also be known as an oblong, a non-square rectangle.
What a Parallelogram is:
A parallelogram is a simple quadrilateral with 2 pairs of parallel sides. The opposite/facing sides of a parallelogram are equal in length and the opposite angles of a parallelogram are equal as well.
What a Trapezoid is:
On a trapezoid, the parallel sides are known as the legs and the other 2 sides are known as the legs. A trapezoid is similar to a trapezium but it has different angles and the parallel sides are uneven in size. There are many types of a trapezoid, one for example is an isosceles trapezoid(having 2 equal sides).
What a Kite is:
A kite shape is a geometric shape with 2 pairs of equal sides, it is also a quadrilateral shape. The inside of a kite shape can contain a perfectly measured circle that just brushes the sides. It can be either a concave or convex shape aswell.
Do you know the difference between a trapezium and a trapezoid?