Question

Theorem 6.2 : If a transversal intersects two parallel lines, then each pair
alternate interior angles is equal.
Now, using the converse of the corresponding angles axiom, can we show the two
lines parallel if a pair of alternate interior angles is equal? In Fig. 6.22, the transversal
PS intersects lines AB and CD at points Q and R respectively such that
$∠$BQR = $∠$QRC.
Is AB II CD?
​

Answer 1

Question⤵️

If a transversal intersects two parallel lines, then each pair

alternate interior angles is equal.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer ⤵️

• See the attachment
• Question solved

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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°

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• 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°

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• Adjacent angle

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

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• 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.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• lenear pair of angles

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

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

TO PROVE :

Angle 2 = Angle 1

Angle 3 = Angle 4

PROOF

Angle 5 = Angle 2 ( Vertical opposite angles)

Angle 5 = Angle 1 (Corrosponding Angles)

=> Angle 2 = Angle 1 -(1)

Angle 6 = Angle 3 (Vertical opposite angles)

Angle 6 = Angle 4 (Corrosponding Angles)

=> Angle 3 = Angle 4 -(2)

In, (1) & (2) we have proved.