Which best explains why all equilateral triangles are similar? all equilateral triangles can be mapped onto each other using dilations. all equilateral triangles can be mapped onto each other using rigid transformations. all equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations. all equilateral triangles are congruent and therefore similar, with side lengths in a 1: 1 ratio.

The correct answer is:

All equilateral triangles can be mapped onto each other using dilations.

The reason that best describes the reason why all equilateral triangles are similar is:

All equilateral triangles can be mapped onto each other using dilations.

Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

In reflection, rotation and translation  and there combinations the location of shape of the figure might appear different.

Hence we could not say that they are similar.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer: a

step-by-step explanation: