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Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of △ABC is 180°.

| Statement | Reason |
|----------------------------------------------------------|------------------------------------------------|
| Points A, B, and C form a triangle. | Given |
| Let DE be a line passing through B and parallel to AC. | Definition of parallel lines |
| ∠3 = ∠5 and ∠1 = ∠4 | |
| m∠1 = m∠4 and m∠3 = m∠5 | |
| m∠4 + m∠2 + m∠5 = 180° | Angle addition and definition of a straight line |
| m∠1 + m∠2 + m∠3 = 180° | Substitution |

Sagot :

GinnyAnsweridn
To show that the sum of the interior angles of [tex]$\triangle ABC$[/tex] is [tex]$180^\circ$[/tex], we need to complete the proof with the correct statements and reasons.

Here's the step-by-step completion:

\begin{tabular}{|l|l|}
\hline
Statement & Reason \\
\hline
Points [tex]$A, B,$[/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]$\angle 3 = \angle 5$[/tex] and [tex]$\angle 1 = \angle 4$[/tex]. & alternate interior angles theorem \\
\hline
[tex]$m \angle 1 = m \angle 4$[/tex] and [tex]$m \angle 3 = m \angle 5$[/tex]. & alternate interior angles are equal \\
\hline
[tex]$m \angle 4 + m \angle 2 + m \angle 5 = 180^\circ$[/tex]. & angle addition and definition of a straight line \\
\hline
[tex]$m \angle 1 + m \angle 2 + m \angle 3 = 180^\circ$[/tex]. & substitution \\
\hline
\end{tabular}

This structured approach, both with statements and reasons, proves that the sum of the interior angles of [tex]$\triangle ABC$[/tex] is [tex]$180^\circ$[/tex].
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