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.

Line \(\mathtt{BD}\) will be a transversal.

2

Draw line \(\mathtt{EC}\) parallel to segment \(\mathtt{AB}\).

Draw transversal \(\mathtt{\overleftrightarrow{AC}}\).

Draw transversal \(\mathtt{\overleftrightarrow{AC}}\).

3

Corresponding angles are congruent.

\(\mathtt{m\color{green}{\measuredangle{ECD}}}\) = \(\mathtt{m\color{green}{\measuredangle{ABC}}}\)

\(\mathtt{m\color{green}{\measuredangle{ECD}}}\) = \(\mathtt{m\color{green}{\measuredangle{ABC}}}\)

4

Alternate interior angles are congruent.

\(\mathtt{m\color{orange}{\measuredangle{ECA}}}\) = \(\mathtt{m\color{orange}{\measuredangle{CAB}}}\)

\(\mathtt{m\color{orange}{\measuredangle{ECA}}}\) = \(\mathtt{m\color{orange}{\measuredangle{CAB}}}\)

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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