Consecutive Interior Angles Theorem
Consecutive Interior Angles
When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.
In the figure, the angles and are consecutive interior angles.
Also the angles and are consecutive interior angles.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
Proof:
Given: , is a transversal
Prove: and are supplementary and and are supplementary.
Statement
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Reason
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1
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,
is a traversal.
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Given
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2
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and
form a linear pair and
and
form a linear pair.
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Definition of
linear pair
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3
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and are supplementary
and are supplementary
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4
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and
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Corresponding Angles Theorem
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5
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and
are supplementary
and
are supplementary.
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Substitution Property
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