# Alternate angles

two nonadjacent angles made by the crossing of two lines by a third line, both angles being either interior or exterior, and being on opposite sides of the third line.

Historical *Examples*

Euclid introduced the subject by the proposition that, if alternate angles are equal, the lines are parallel.

The Teaching of Geometry David Eugene Smith

And “if the lines are parallel, are alternate angles necessarily equal?”

Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 Various

The sides of the octagon are equal, and the alternate angles coincident.

The Prehistoric World E. A. Allen

We may now state Prop. 16 thus:—If two straight lines which meet are cut by a transversal, their alternate angles are unequal.

Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 Various

That is to say, “If alternate angles are unequal, do the lines meet?”

Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 Various

Frustules oblong or quadrate, adnate in filaments, attached by alternate angles and finally separating.

The Diatomaceae of Philadelphia and Vicinity Charles Sumner Boyer

plural **noun**

two angles at opposite ends and on opposite sides of a transversal cutting two lines

alternate angles

Two angles formed on opposite sides of a line that crosses two other lines. The angles are both exterior or both interior, but not adjacent.

Tagged: a

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