Question

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.

Answer 1

In the solution we will use the concept of same base and same parallels which states that when two figures have a similar side which is base and lines are parallel opposite to common base.

Complete step-by-step solution
In figure (i), the $\Delta PDC$ and trapezium $ABCD$ both are lying on the similar base $DC$ and among the same parallel lines which are $DC$ and $AB$.
Therefore, both the figures lie on the same base and between the same parallels line.

In figure (ii), the trapezium $SMNR$ and parallelogram $PQRS$ both are lying on the same base $SR$ but not between the same parallel lines.
Therefore, both the figures lie on the same base but not between the same parallels line.

In figure (iii), the $\Delta RTQ$ and parallelogram $PQRS$ both are lying on the same base $QR$ and between the same parallel lines $QR$ and $PS$.
Therefore, both the figures lie on the same base and between the same parallels line.

In figure (iv), the $\Delta PQR$ and parallelogram $ABCD$ both are not lying on the same base but between the same parallel lines $BC$ and $AD$.
Therefore, both the figures are not lying on the same base.

In figure (v), the trapezium $APCD$ and quadrilateral $ABQD$ both are lying on the same base $AD$ and between the same parallel lines $AD$ and $BQ$.
Therefore, both the figures lie on the same base and between the same parallels line.

In figure (vi), the parallelogram $ABCD$ and parallelogram $PQRS$ both are not lying on the same base $SR$ and don’t lie among the same parallel lines.
Therefore, both figures don’t lie on the same base.

Note: In such types of questions, make sure to use the same base and same parallel concept in any geometric figures i.e “when two figures have a similar side which is base and lines are parallel opposite to common base”.