Answer:
Interior angles are congruent.
Step-by-step explanation:
We see that angles 3,4,5,6 are between the two parallel lines . These angles are called interior angles.
Angles 3,6 are opposite and do not share the same vertex.
Similarly angles 4 and 5 do not share the same vertex.
They are congruent.
If we look closely we see that angles 3 &4 and angles 5&6 are supplementary angles.
i.e they together make up the 180 degrees on the straight line.
On the outer sides of the parallel lines angles 1&2 and angles 7 & 8 are exterior angles
which also make supplementary angles on the parallel lines.
From the diagram we see that
∠ 5= ∠7
and
∠6 = ∠ 8
as the corresponding angles are equal
∠8=∠3
∠7=∠4
As they are opposite angles
Similarly
∠1=∠6
∠2=∠5 ( opposite angles)
From above
∠5=∠7
but ∠7= ∠4
therefore
∠ 5= ∠4-----------------A
Also
∠6 = ∠ 8
but ∠8=∠3
therefore
∠6=∠8----------------------B
From An and B we conclude interior angles are congruent
