Which of the following are parts of a two-column proof? select all that apply.

statements
reasons
prove statement
given statement

The correct answer is:

All of the options are in a two-column proof.

Explanation:

In a two-column proof, we start with a list of "given" statements. This is the series of statements we begin with in the proof.

Below this, we are given a "prove" statement; this is the statement we are to be working to prove throughout the proof.

We then write two columns; one is labeled "statements," in which we will use steps to get from the "given" to the "prove" statement.

The second column is labeled "reasons" or "justifications"; in this column we justify using theorems, definitions and postulates the statements we use in the proof.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240