CK12 - Geometry

The correspondingangleyou just filledin is also verticalto. Sinceverticalanglesare congruent,you

can conclude.

This exampleis very similarto the proofof the alternateexterioranglesTheorem.Herewe writeout the
theoremin whole:

AlternateExteriorAnglesTheoremIf two parallellinesare crossedby a transversal,

then alternateexterioranglesare congruent.

We omit the proofhere,but note that you can provealternateexterioranglesare congruentby followingthe
methodof example4, but not usingany particularmeasuresfor the angles.

ConsecutiveInteriorAnglesTheorem

The last categoryof anglesto explorein this lessonis consecutiveinteriorangles.Theyfall on the interior
of the parallellines and are on the sameside of the transversal.Use your knowledgeof correspondingangles
to identifytheir mathematicalrelationship.

Example 5

Lines and in the diagrambeloware parallel.If the anglecorrespondingto measures

whatis?

This processshouldnow seemfamiliar. The given angleis adjacentto and they form a linearpair.

Therefore,the anglesare supplementary. So, to find , subtract from

This exampleshowsthat if two parallellinesare cut by a transversal,the consecutiveinterioranglesare

supplementary;they sum to This is calledthe ConsecutiveInteriorAnglesTheorem.We restateit
here for clarity.