Question

Theorem 6.3: If a transversal intersects two lines such that a pair of alternative interior angles is equal, then the two lines are parallel.

In a similar way, you can obtain the following two theorems related to interior angle on the same side of the transversal.

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Answer 1

Question⤵️

If a transversal intersects two parallel lines, then each pair

alternate interior angles is equal.

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Answer ⤵️

See the attachment

Question solved

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• All necessary Formulas

complementary angle

The sum of 2 numbers= 90

example a+b=90°

how to find "a" if a is not mentioned

Given

A= ?

b = 40

a+40=90°

a=90-40°

a=50°

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• supplementary angle

The sum of two numbers= 180°

example= a+b=180

how to find "a" if a is not mentioned

Given

A= ?

b = 40

a+40=180°

a=180-40°

a=140°

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• Adjacent angle

If there is a common ray between ${\bf&#x2220}$a and ${\bf&#x2220}$b so it is a adjacent angle.

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• Vertical opposite angle

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

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• lenear pair of angles

Here ${\bf&#x2220}$a+${\bf&#x2220}$b=180°

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Answer 2

A transversal AB intersects two lines PQ and RS such that

∠PLM = ∠SML

To Prove: PQ ||RS

Proof: ∠PLM = ∠SML…equation (i) (Given)

∠SML = ∠RMB …………equation (ii) (vertically opposite angles)

From equations (i) and (ii);

∠PLM = ∠RMB

But these are corresponding angles.

We know that if a transversal intersects two lines such that a pair of alternate angles are equal, then the two lines are parallel to each other.

Hence, PQ║RS Proved.