Question

Fill in the blank. Given V below, you can conclude that OS is congruent to:

A. NR
B. VU
C. NT
D. OV

Answer 1

Given angle V below, you can conclude that angle OS is congruent to
`(\boxed{\text{D. OV}}\).`

Step-by-step explanation:

In the provided diagram, let
`\( \angle V \)` be denoted as
`\( \angle V = \angle NR \).`The congruence of corresponding angles in a geometric figure implies the congruence of the associated line segments. Therefore,
`\( OS \)` is congruent to
`\( NR \).`

Next, consider the given options. Option D,
`\( OV \)`, corresponds to
`\( OS \)` in the figure. By the Corresponding Angles Postulate,
`\( \angle OS \)` is congruent to
`\( \angle OV \).` Thus, the correct conclusion is that
`\( \angle OS \)` is congruent to
`\( \angle OV \),` and the answer is D.

To further validate this, one can use the definition of congruent angles. Two angles are congruent if and only if they have the same measure. In this case
`, \( \angle OS \)` and
`\( \angle OV \)` share the same measure, confirming the congruence. In mathematical terms, this can be expressed as
`\( \angle OS \cong \angle OV \)` due to the Corresponding Angles Postulate. Therefore, the correct answer is option D,
`\( OV \).`