Question

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

Answer 1

Answer:

same base

Step-by-step explanation:

Two  figures are said to be on the same base and between the same parallels if they have a common base or side and the vertices opposite to the common base of each  figure on a line parallel to the base.

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Solution:

In Figure  (i) , ∆PDC and trapezium ABCD are lying on the same base PC and between the same parallels AB and DC.

 

In Figure (ii) it can be observed that parallelogram PQRS and trapezium MNRS have a common base RS but their vertices (opposite to the common base) P, Q of parallelogram and  M , N of trapezium are not lying on the same line. Thus, they are not lying between the same parallels.

 

In figure (iii) ∆TRQ and parallelogram PQRS are lying on the same base RQ and between the same parallels are RQ and SP.

 

In figure (iv) it can be observed that parallelogram ABCD and ∆PQR are lying between the same parallels AC and BC but they do not have any common base.

 

In figure (v) parallelograms ABCD & APQD are lying  on the same base and between the same parallel AD and BQ.

 

In figure (vi) it can be observed that parallelogram PBCS and PQRS are lying on the same base PS, but they do not lie between the same parallels. Similarly , parallelograms AWARD and PQRS  are lying  on the same base QR but they do not lie between the same parallels.

 

Hence, figures (i), (iii) & (v)  lie on the same base and between the same parallels.

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Answer 2

the same base is DC and parallel line are DCparallel to AB