Vertical Angle Theorem
Press on the numbers to see the steps of the proof.
1
$$\mathtt{\overleftrightarrow{AB}}$$ and $$\mathtt{\overleftrightarrow{CD}}$$ intersect at point $$\mathtt{E}$$.
And $$\mathtt{m\color{purple}{\measuredangle{CEA}}}$$ + $$\mathtt{m\color{green}{\measuredangle{AED}}}$$ = $$\mathtt{\color{blue}{180^\circ}}$$.
2
Similarly, $$\mathtt{m\color{green}{\measuredangle{AED}}}$$ + $$\mathtt{m\color{orange}{\measuredangle{DEB}}}$$ = $$\mathtt{\color{blue}{180^\circ}}$$,
because those angles also form a linear pair.
3
This means that:
$$\mathtt{m\color{purple}{\measuredangle{CEA}}}$$ + $$\mathtt{m\color{green}{\measuredangle{AED}}}$$ = $$\mathtt{m\color{orange}{\measuredangle{DEB}}}$$ + $$\mathtt{m\color{green}{\measuredangle{AED}}}$$.
4
If $$\mathtt{\color{purple}{a} + \color{green}{b} = \color{orange}{c} + \color{green}{b}}$$, then $$\mathtt{\color{purple}{a} = \color{orange}{c}}$$.
So, $$\mathtt{m\measuredangle{CEA}}$$ = $$\mathtt{m\measuredangle{DEB}}$$.
5
The same process can be used to show that
$$\mathtt{m\measuredangle{AED}}$$ = $$\mathtt{m\measuredangle{BEC}}$$.
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