Question

write an indirect proof for the following conditional about the figure. if ∠efg and ∠hfj are vertical angles, then x≠3y. to prove the given conditional by contradiction, assume that ∠efg and ∠hfj are vertical angles and that x = 3y. because ∠efg and ∠hfj are vertical angles, they are congruent. this means their measures are equal, yielding the equation x + y = 2x - y. (type an equation using x and y as the variables. do not include the degree symbol in your answer. do not simplify.) using the assumption to rewrite this equation in terms of y alone and then separately simplifying each side produces the equation 4y = 5y. it follows that y = , and so x = . (simplify your answers.)

Explanation:

Step1: Substitute x = 3y into x + y = 2x - y

Substitute $x = 3y$ into the equation $x + y=2x - y$. We get $(3y)+y = 2(3y)-y$.

Step2: Simplify both sides of the equation

On the left - hand side, $(3y)+y=4y$. On the right - hand side, $2(3y)-y = 6y - y=5y$. So the equation becomes $4y = 5y$.

Step3: Solve for y

Subtract $4y$ from both sides of the equation $4y = 5y$. We have $4y-4y=5y - 4y$, which gives $y = 0$.

Step4: Solve for x

Since $x = 3y$ and $y = 0$, then $x=3\times0 = 0$.

Answer:

$y = 0$, $x = 0$