Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Select the correct answer from each drop-down menu.

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 :

GinnyAnswer
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].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.