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Similar Triangles Formed Between Parallel Lines

When two lines cross each other at a point A, angles on opposite sides of the point are the same.

If parallel lines are drawn to construct two triangles, with one angle in each triangle the angle at A, then the triangles will be similar. In the diagram below, triangles ABC and tirangles ADE are similar.

This is because the triangles have identical angles.

Angle BAC = Angle DAE

Angle EDA = Angle ABC (corresponding angles in a Z shape)

Angle DEA = Angle ACB (corresponding angles in a Z shape)

This means that

Example

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