triangle sum theorem triangle sum theorem
Triangle Sum + Exterior Angle Theorem
Press on the numbers to see the steps of the proof.
1
Start with \(\Delta\mathtt{ABC}\). Extend \(\mathtt{\overline{BC}}\) to point \(\mathtt{D}\).
Line \(\mathtt{BD}\) will be a transversal.
2
Draw line \(\mathtt{EC}\) parallel to segment \(\mathtt{AB}\).
Draw transversal \(\mathtt{\overleftrightarrow{AC}}\).
3
Corresponding angles are congruent.
\(\mathtt{m\color{green}{\measuredangle{ECD}}}\) = \(\mathtt{m\color{green}{\measuredangle{ABC}}}\)
4
Alternate interior angles are congruent.
\(\mathtt{m\color{orange}{\measuredangle{ECA}}}\) = \(\mathtt{m\color{orange}{\measuredangle{CAB}}}\)
5
The exterior angle is congruent to the two remote interior angles. And, \(\mathtt{m\color{orange}{\measuredangle{A}}}\) + \(\mathtt{m\color{green}{\measuredangle{B}}}\) + \(\mathtt{m\color{slateblue}{\measuredangle{C}}}\) = \(\mathtt{180^\circ}\).
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