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 vertic this means their measures are equi (type an equation using x and y as th using the assumption to rewrite this e it follows that y = 0, and so x = 0 (simplify your answers.) this means that m∠efg = 0 and m (type integers or decimals. do not inc it follows from this that ej and gh

Explanation:

Step1: Assume the opposite

Assume $\angle EFG$ and $\angle HFJ$ are vertical - angles and $x = 3y$.

Step2: Use the property of vertical angles

Since vertical angles are equal, we have $x + y=2x - y$.

Step3: Substitute $x = 3y$ into the equation

Substitute $x = 3y$ into $x + y=2x - y$, we get $3y + y=2(3y)-y$.

Step4: Simplify the equation

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

Step5: Solve for $y$

Subtract $4y$ from both sides of the equation $4y = 5y$, we get $0=y$.

Step6: Solve for $x$

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

Step7: Analyze the angle measures

If $x = 0$ and $y = 0$, then $m\angle EFG=x + y=0$ and $m\angle HFJ=2x - y=0$. This is a contradiction because non - degenerate vertical angles have non - zero measures.

Answer:

The original statement "If $\angle EFG$ and $\angle HFJ$ are vertical angles, then $x
eq3y$" is true.