Theorem - III:
If a transversal intersects a pair of parallel lines, then the interior angles on the same side of the transversal are supplementary.
Hypothesis:
l // m and a transversal 'p' intersects the two lines so that ÐA and ÐB are a pair of interior angles on the same side of the transversal and ÐE and ÐF is the other such pair.
Conclusion:
a. ÐA + ÐB = 180°.
b. ÐE + ÐF = 180°
Proof:
ÐA and ÐH form a linear pair,
Therefore, ÐA + ÐH = 180°
But ÐH = ÐB (By the axiom of corresponding angles).
Therefore, Putting ÐB in the place of ÐH, we get
ÐA + ÐB = 180°
Similarly we can also show thatÐ
E + ÐF = 180°.,br>
Note:
According to the axiom-3 on corresponding angles, we know that if a transversal intersects two parallel lines, then the corresponding angles will be equal.
Directions: Draw parallel lines and a transversal and show that the interior angles on the same side of the transversal are supplementary.
|
