Chapter 11.1, Problem 30PPS

To determine

If the pairs of opposite sides in given quadrilateral are parallel based on the given figure.

Answer to Problem 30PPS

Pair p and q of opposite side is parallel but pair r and s or opposite sides is NOT parallel.

Explanation of Solution

Given information: Given following figure, showing forming a quadrilateral there:

  

Concept used:

By property of parallel lines, if two parallel lines are cut be a transversal, then the corresponding angles, thus forming are always equal to each other. And exterior corresponding angles on the same side of a transversal is 180 degree always.

Calculation:

Here as two lines r and s are being cut by a transversal p , the two corresponding angles ${60}^0$ and ${62}^0$ are not equal to each other. Hence, lines r and s are not parallel. Similarly, when these two lines p and q are being cut by a transversal r , the sum of two exterior corresponding angles ${120}^0$ and ${118}^0$ , on the same side of this transversal is 180 degree, so lines p and q are parallel.

Conclusion:

By above calculation, it is concluded that only one pair of opposite sides p and q is parallel but another pair of opposite sides r and s is not parallel.