Question

Explain Theorem 6.4 with proof.
STD.9th
(Hint. If a transversal intersects two parallel lines than each pair of interior angles on the same side of transversal are supplementary.)​

Answer 1

Answer:

If a ray stands on a line, then the sum of two adjacent angles so formed id 180 degree. (Axiom 6.1)

Step-by-step explanation:

When the sum of two adjacent angles is 180 degree, the they are called a linear pair of angles.

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Answer 2

Explain Theorem 6.4 with proof.

Hint. If a transversal intersects two parallel lines than each pair of interior angles on the same side of transversal are supplementary.

Given : Two parallel lines AB and CD and transversal PS intersects AB at Q and CD at R.

To prove : Sum of interior angles on the same side of transversal is supplementary.

i.e, Angle AQR + Angle CRQ = 180°

Angle BQR + Angle DRQ = 180°

Proof :

Angle AQP = Angle CRQ (corresponding angles) -------- (1)

Angle AQP + Angle AQR = 180° (Linear Pair)-------- (2)

Putting (1) in (2)

Angle AQP + Angle CRQ = 180°

Similarly it can be proved that,

Angle BQR + Angle DRQ = 180°

Sum of interior angles on the same side of transversal is 180°.

Hence proved.

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