Question

Lines x and y intersect to make two pairs of vertical angles, q, s and r, t. Fill in the blank space in the given proof to prove ∠q ≅ ∠s. A) Transitive property B) Addition property of equality C) Subtraction property of equality D) Substitution property

Answer 1

C

Explanation:

Because I am a genius

Answer 2

C) Subtraction property of equality.

Explanation:

Given that, two lines
`x` and
`y` intersect to make pairs of vertical angles:

`\angle q, \angle s` and
`\angle r, \angle t`.

Kindly refer to the attached image for details of the given angles and lines.

Proof that
`\angle q\cong \angle s` :

`\begin{center}\begin{tabular}{ c c}Statements & Reasons \\ m\angle q+m\angle r=180^\circ & \angle q\ and\ \angle r\ are\ supplementary \\ m\angle r+m\angle s=180^\circ & \angle r\ and\ \angle s\ are\ supplementary \\ \angle q+\angle r=\angle q+\angle r & Algebraic substitution \\ m\angle q = m\angle s & Subtraction property of equality\end{tabular}\end{center}`

Here, subtraction property of equality is used in the last step shown in the above.

As per the Subtraction property of equality, when some value is subtracted from both the sides of the equality, equality remains the same.