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Lesson: Geometry - 04

Vertical Angles

[Page 4 of 30]

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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