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# 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.

**Solution:**

i)

Yes, Figure (i) lies on the same base and between the same set of parallel lines.

It can be observed that trapezium ABCD and triangle PCD have a common base CD and these are lying between the same set of parallel lines AB and CD.

ii)

No, Figure (ii) does not satisfy the condition of having a common base and lying between the same set of parallel lines.

It can be observed that parallelogram PQRS and trapezium MNRS have a common base RS. However, their vertices, (i.e., opposite to the common base) P, Q of parallelogram and M, N of trapezium do not lie on the same line. Hence, parallelogram PQRS and trapezium MNRS do not lie between the same set of parallel lines.

iii)

Yes, Figure (iii) lies on the same base and between the same set of parallel lines.

It can be observed that parallelogram PQRS and triangle QTR have a common base QR and they are lying between the same set of parallel lines PS and QR.

iv)

No, Figure (iv) does not satisfy the condition of having a common base and lying between the same set of parallel lines.

It can be observed that parallelogram ABCD and triangle PQR are lying between the same set of parallel lines AD and BC. However, these do not have any common base.

v)

Yes, Figure (v) lies on the same base and between the same set of parallel lines.

It can be observed that parallelogram ABCD and parallelogram APQD have a common base AD and these are lying between the same set of parallel lines AD and BQ.

vi)

No, Figure (vi) does not satisfy the condition of having a common base and lying between the same set of parallel lines.

It can be observed that parallelogram PBCS and PQRS are lying on the same base PS. However, these do not lie between the same set of parallel lines.

Note: Any two parallelograms in the given figure will not lie between same parallel lines.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 9

**Video Solution:**

## 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.

NCERT Maths Solutions Class 9 Chapter 9 Exercise 9.1 Question 1

**Summary:**

Figure (i), Figure (iii), and Figure (v) lie on the same base and between the same set of parallel lines.

**☛ Related Questions:**

- If E, F, G, and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = 1/2 ar (ABCD).
- P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).
- In Fig. 9.16, P is a point in the interior of a parallelogram ABCD. Show that (i) ar (APB) + ar (PCD) = 1/2 ar (ABCD) (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) [Hint: Through P, draw a line parallel to AB.]
- In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) ar (PQRS) = ar (ABRS) (ii) ar (AXS) = 1/2 ar (PQRS)

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