State whether the following statement is true or false.

When a transversal cuts two parallel lines, the interior angles on the same side of the transversal are equal.

Question

State whether the following statement is true or false.When a transversal cuts two parallel lines, the interior angles on the same side of the transversal are equal.

Accepted Answer

It is given that a transversal line cuts two parallel lines.We know that a transversal line intersects two other lines at two different points within the same plane. The angles in corresponding corners on a transversal are known as corresponding angles.

∠1 & ∠5
  and

∠2 & ∠6
   in the following diagram are examples of corresponding angles.The two lines will be parallel if the corresponding angles are equal, and corresponding angles will also be equal if the lines are parallel. Co-interior angles are those that are located between two lines and on the same transverse sides of a line.Co-interior angles in the above figure are

∠3 & ∠6
  and

∠4 & ∠5.
 The two lines will be parallel if the sum of the co-interior angles is

180
    °
   
   ,
  and vice versa if the lines are parallel.The interior angles on the same side of the transversal will be

180
    °
   
   ,
 if two parallel lines are intersected by it. Therefore, they won't be equal unless each angle

90
    °
   
   .
 Thus, they do not necessarily need to be equal. Therefore, when a transversal cuts two parallel lines, the interior angles on the same side of the transversal may not equal.Thus, the given statement is not true.Hence, option (2) is correct.

State whether the following statement is true or false.

When a transversal cuts two parallel lines, the interior angles on the same side of the transversal are equal.

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