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nata0808 [166]
3 years ago
13

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

Mathematics
1 answer:
bonufazy [111]3 years ago
5 0

Answer:

C) Subtraction property of equality.

Step-by-step 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 <em>Subtraction property </em>of equality, when some value is subtracted from both the sides of the equality, equality remains the same.

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