Answered

Connect with a global community of experts on IDNLearn.com. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

Select the correct answer from each drop-down menu.

Points [tex]\(A, B\)[/tex], and [tex]\(C\)[/tex] form a triangle. Complete the statements to prove that the sum of the interior angles of [tex]\(\triangle ABC\)[/tex] is [tex]\(180^\circ\)[/tex].

[tex]\[
\begin{tabular}{|c|c|}
\hline
Statement & Reason \\
\hline
Points \(A, B\), and \(C\) form a triangle. & Given \\
\hline
Let \(\overline{DE}\) be a line passing through \(B\) and parallel to \(\overline{AC}\). & Definition of parallel lines \\
\hline
\(\angle 3 \cong \angle 5\) and \(\angle 1 \cong \angle 4\) & Corresponding angles are congruent \\
\hline
\(m \angle 1 = m \angle 4\) and \(m \angle 3 = m \angle 5\) & Definition of congruent angles \\
\hline
\(m \angle 4 + m \angle 2 + m \angle 5 = 180^\circ\) & Angle addition and definition of a straight line \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
Here’s the corrected version of the solution to prove that the sum of the interior angles of [tex]\(\triangle ABC\)[/tex] is [tex]\(180^\circ\)[/tex]:

\begin{tabular}{|c|c|}
\hline
Statement & Reason \\
\hline
Points [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] form a triangle. & Given \\
\hline
Let [tex]\(\overline{DE}\)[/tex] be a line passing through [tex]\(B\)[/tex] and parallel to [tex]\(\overline{AC}\)[/tex]. & Definition of parallel lines \\
\hline
[tex]\(\angle 3 \cong \angle 5\)[/tex] and [tex]\(\angle 1 \cong \angle 4\)[/tex] & Alternate interior angles are congruent \\
\hline
[tex]\(m \angle 1 = m \angle 4\)[/tex] and [tex]\(m \angle 3 = m \angle 5\)[/tex] & Definition of congruent angles \\
\hline
[tex]\(m \angle 4 + m \angle 2 + m \angle 5 = 180^\circ\)[/tex] & Angle addition and definition of a straight line \\
\hline
\end{tabular}

By these steps, you can see we are using geometric properties and definitions to show that the interior angles of [tex]\(\triangle ABC\)[/tex] add up to [tex]\(180^\circ\)[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.