Alternate Exterior Angles Theorem states that "Alternate Exterior Angles formed by two parallel lines and a transversal are always congruent".
In the figure given above, angles 2 and 8 are alternate exterior angles. Angles 1 and 7 are also alternate exterior angles. Therefore, $\angle$2 = $\angle$8 and $\angle$1 = $\angle$7.
One way to easily find the alternate exterior angles is that they are the vertical angles of the alternate interior angles. Alternate exterior angles are equal to one another.
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If two parallel line segments or rays are cut by a transversal, the alternate exterior angles are congruent.
Line p is parallel to line q with the transversal l, as shown in the figure given below.
|1||p | | q with the transversal l||Given|
|2||$\angle$2 is congruent to $\angle$6||Parallel Lines Postulate|
|3||$\angle$6 is congruent to $\angle$8||Vertical Angle Theorem|
|4||$\angle$2 is congruent to $\angle$8||Using Transitive Property|
Therefore, the alternate exterior angles are congruent.
$\angle$2 is congruent to $\angle$8
$\angle$6 is congruent to $\angle$8
||Vertical Angle Theorem|
|Step 3:||$\angle$2 is congruent to $\angle$6||
p | | q with the transversal l
|From Step 2 and Step 3
Parallel Line Postulate
Therefore, the lines are parallel.Hence Proved.
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