Question

State the following statement is true or false
If two parallel lines are cut by transversal, then pair of alternate interior angles not equal
A) True
B) False

Answer 1

Hint: According to the question given in the question we have to determine that the statement If two parallel lines are cut by transversal, then a pair of alternate interior angles not equal is true or false. So, first of all we have to draw two parallel lines and a transversal line which intersects the two parallel lines which is as below:

Hence, from in the diagram above lines P and Q are parallel to each other and a transversal line R intersects the both of the parallel lines P and Q and all the interior angles are $\angle 1,\angle 2,\angle 3,\angle 4,\angle 5,\angle 6,\angle 7,$ and $\angle 8$.
Now, we have to use the transversal theorem to determine when two parallel lines are cut by transversal, then pair of alternate interior angles not equal is true or not which is explained below:
According to transversal theorem if two parallel lines are intersected by another transversal line then the alternate interior angles formed are congruent or we can say equal to each other.

Complete step-by-step solution:
Step 1: First of all we have to draw the diagram for If two parallel lines are cut by transversal, then a pair of alternate interior angles not equal is true or false. So, first of all we have to draw two parallel lines and a transversal line which intersects the two parallel lines as mentioned in the solution hint. Hence,

Step 2: Now, as we know that when two lines are intersected by a transversal line, then pairs of angles on one side of the transversal line which is R and inside the two lines P and Q are known as the consecutive interior angles. Hence, from the diagram as mentioned in the solution step 1,

$
   \Rightarrow \angle 1 = \angle 5, \\
   \Rightarrow \angle 3 = \angle 7, \\
   \Rightarrow \angle 2 = \angle 6,and \\
   \Rightarrow \angle 4 = \angle 8
 $
Hence, If two parallel lines are cut by transversal, then a pair of alternate interior angles not equal is false.

Therefore option (B) is correct.

Note: If two parallel lines are intersected by another transversal line then the alternate interior angles formed are congruent or we can say equal to each other.