Axiom - 4:
If a transversal intersects two coplanar lines, so that a pair of corresponding angles are equal, then the two lines are parallel.
Theorem - IV:
If a transversal intersects two coplanar lines in such a way that pair of Alternate angles are equal, then the two lines are parallel.
Hypothesis:
'l' and 'm' are two coplanar lines. 'p' is the transversal intersecting them so that a pair of alternate angles ÐA = ÐB.
Conclusion:
l // m.
Proof:
Let ÐC be the vertically opposite angle to ÐA.
Then, ÐA = ÐC.
but ÐA = ÐB given,
Therefore, ÐB = ÐC.
That is the corresponding angles are equal.
Therefore, by axiom-4 'l' must be parallel to 'm'.
Hence l // m.
Directions: Draw a pair of parallel lines and a transversal and show that the corresponding angles are equal.
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