Consider the rotational symmetry of equilateral triangle
abc
what is the order of rotational symmetry for triangle abc?
1

Order of rotational symmetry is 1.

Step-by-step explanation:

We know that an equilateral triangle has all its angle as 60° as all the sides of the triangle are similar.

The triangle is completely similar from all the vertices. Order of rotational symmetry is defined as the number of times the diagram or figure needs to be rotated so as to get back the original picture.

So here let the three vertices be A,B,C. When we rotate the figure once by 60° to get the next vertice we see that the obtained diagram is completely similar to the original one. So one rotation i sufficient to obtain the original figure hence the order is 1.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.