Triangles similar to the same triangle are to each other. a. congruentb) similarc) closed) parallel

Similar.

First of all, options C and D make no sense, since we don't have a concept for triangles being "close" or "parallel" to each other.

Now, two triangles are similar if one is the scaled version of each other. As a consequence, the triangles have the same angles, and the correspondant sides are in the same proportion.

So, assume that we start from the original triangle ABC. We build two other triangles, DEF and GHI, both similar to ABC.

This means that the correspondant sides of ABC and DEF are in the same proportion, say . This means that

Similarly, the correspondant sides of ABC and GHI are in the same proportion, say . This means that

Now, the question is: are DEF and GHI similar? The answer is yes, because we can perform the following transformation: let's start for example from the side GH:

This means that

and thus the sides of DEF and GHI are in the same proportion, which means that they are similar.

can you complete your sentence? i could !

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0