Question

which pair of the dotted line segments in the following figures are parallel give reason
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Answer 1

Step-by-step explanation:

this question, we are given a quadrilateral with four angles between their sides. A quadrilateral is a polygon with four sides/edges and four vertices/corners. Now, in this question, we are going to check that with which sides the line AB and BC will be parallel. To check this, we will make use of the fact if the sum of the interior angles between any two given lines is 180o.

If this sum will be equal to 180o

then the lines will be parallel and if it is not equal to 180o

then the given pair of lines will be non-parallel. So, first, let us consider the lines AB and CD. The line BC can act as a joining line. Now, we will calculate the sum of the interior angles. In this case, the interior angles will be ∠ABC and ∠DCB.

The sum of the interior angles is given by:

Sum =∠ABC+∠DCBSum =65o+115oSum =180o

As the sum between them is 180o,

the lines AB and CD will be parallel to each other.

Now, we will check the same for line AD and BC. In this case, line AB can act as a joining line. The interior angles, in this case, are ∠DAB and ∠ABC.

The sum of the interior angles will be given by:

Sum =∠DAB+∠ABCSum =115o+65oSum =180o

As the sum of the interior angles is 180o,

the lines AD and BC are parallel.

Thus, AB||CD and AD||BC.