Question

Select the reason that best supports Statement 8 in the given proof.

Answer 1

Therefore, the correct answer is:

B. Division Property of Equality

This is the reason that supports Statement 8 in the proof, as it explains how we go from
`\( 5x = 10 \)` to
`\( x = 2 \).`

The provided image shows a geometric proof with steps leading up to the conclusion that
`\( x = 2 \)`. The last step, step 8, concludes
`\( x = 2 \)` and asks for the reason supporting this statement. To find the reason, let's examine the previous step.

Step 7 is the equation
`\( 5x = 10 \)`. To isolate
`\( x \)` and solve for it, we divide both sides of the equation by 5. This is the Division Property of Equality, which states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.

Therefore, the correct answer is:

B. Division Property of Equality

This is the reason that supports Statement 8 in the proof, as it explains how we go from
`\( 5x = 10 \)` to
`\( x = 2 \).`

Answer 2

Given

Ray RV bisects angle ABC

`\begin{gathered} m\angle ABV=7x-3 \\ m\angle VBC=2x+7 \end{gathered}`

Find

Select the reason that best supports statement 8 in the given proof.

Step-by-step explanation

Given

Ray RV bisects angle ABC

so , by definition of angle bisect

`m\angle ABV=m\angle VBC`

by substitution ,

`7x-3=2x+7`

addition property of equality

`7x=2x+10`

now, by substitution property of equality ,

`5x=10`

and last , by division property of equality

`x=2`

Final Answer

Therefore , the correct option is B.