Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.

we have given that δ abc is similar to δ cbd and δ abc is similar to δ acd according to the attached picture.

because of the similarity the corresponding sides are proportional. then a/c = f/a

and b/e = c/b. if we cross multiply, we'll get

a² = cf and b² = ce

if we add these equalities together, we'll get

a² + b² = c (f + e)

from the beginning, we know that c = e+f

then, the final result is:

a² + b² = c²

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

1; 35 is the ratio

step-by-step explanation: