NCERT Solutions for Class 9 Clat Chapter 11 Constructions

Constructions Here is the CBSE Clat Chapter 11 for Class 9 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 9 Clat Constructions Chapter 11 NCERT Solutions for Class 9 Clat Constructions Chapter 11 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 9 Clat.

Question 1

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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) ΔPDC and quadrilateral ABCD lie on the same base DC and between the same parallels DC and AB.
(iii) ΔTRQ and parallelogram SRQP lie on the same base RQ and between the same parallels RQ and SP.

(v) Quadrilaterals APCD and ABQD lie on the same base AD and between the same parallels AD and BQ.

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NCERT Solutions for Class 9 Clat Chapter 11 Constructions

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.

In figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH) = $1 half$ ar(ABCD).

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(ΔAPB) = ar{ΔBQC).

In figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:

(i) ar(|| gm PQRS) = ar(|| gm ABRS)

(ii) $ar left parenthesis increment AXS right parenthesis equals 1 half ar left parenthesis space parallel to space gm space PQRS right parenthesis.$

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Prove that of all parallelograms of which the sides are given, the parallelogram which is a rectangle, has the greatest area.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

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NCERT Solutions for Class 9 Clat Chapter 11 Constructions

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.

In figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH) = ar(ABCD).

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(ΔAPB) = ar{ΔBQC).

In figure, P is a point in the interior of a parallelogram ABCD. Show that:(1) ar((ii) ar(ΔAPD) + ar(ΔPBC) = ar(ΔAPB) + ar(ΔPCD). [CBSE 2012 (March)][Hint. Through P, draw a line parallel to AB.]

In figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that: (i) ar(|| gm PQRS) = ar(|| gm ABRS)(ii)

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Prove that of all parallelograms of which the sides are given, the parallelogram which is a rectangle, has the greatest area.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar(EFGH) = $1 half$ ar(ABCD).

In figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:

(i) ar(|| gm PQRS) = ar(|| gm ABRS)

(ii) $ar left parenthesis increment AXS right parenthesis equals 1 half ar left parenthesis space parallel to space gm space PQRS right parenthesis.$