When lines intersect they form opposite (or vertical)
angles. In the figure below, there are two pairs of opposite angles: ? AEB
and ? DEC,
and? DEA
and ? CEB.
Notice that in the figure below the angles across
from each other are each supplementary to the same angle. For example,
? AEB
and ?BEC
are supplementary, and ? AEB's
opposite angle, ? DEC,
is also supplementary to ? BEC.
This leads to the following conclusion.
All
opposite, or vertical, angles are equal.
? DEA
and ? CEB
are each supplementary to ? AEB.
So each of these angles equals 180° – ? AEB.
? AEB
and ? DEC
are each supplementary to ? DEA.
So each of these angles equals 180° – ? AEB.
Therefore, ? DEA
= ? CEB
and ? AEB
= ? DEC.
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