FRANK Solutions for Class 9 Maths Chapter 19 - Quadrilaterals

If you are given the measure of one angle of a parallelogram, can you find the measure of the remaining angles? You can by referring to our Frank Solutions for ICSE Class 9 Mathematics Chapter 19 Quadrilaterals during revision. Further, you can practise Maths questions and answers on how to prove that the given figure is a parallelogram or a rectangle.

The Frank textbook solutions at the TopperLearning portal even includes problems on providing proofs to show that the given quadrilateral is a rhombus. If you are looking for more such ICSE Class 9 Maths chapter solutions, check the Selina solutions and solved sample question papers.

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Chapter 19 - Quadrilaterals Exercise Ex. 19.1

Question 1(a)

In the following figures, find the remaining angles of the  parallelogram

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 1(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 1(b)

In the following figures, find the remaining angles of the  parallelogram

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 1(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 1(c)

In the following figures, find the remaining angles of the  parallelogram

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 1(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 1(d)

In the following figures, find the remaining angles of the  parallelogram

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 1(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 1(e)

In the following figures, find the remaining angles of the  parallelogram

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 1(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 2
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 2
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 3

The consecutive angles of a parallelogram are in the ratio 3:6. Calculate the measures of all the angles of the parallelogram.

Solution 3

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 4

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 4

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 5

In the given figure, ABCD is a parallelogram, find the values of x and y.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 6

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 7

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 8
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 8
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 9
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 9
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 10
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 10
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 12

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 13

In the given figure, MP is the bisector of P and RN is the bisector of R of parallelogram PQRS. Prove that PMRN is a parallelogram.

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 13

 

Construction: Join PR.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 14

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Chapter 19 - Quadrilaterals Exercise Ex. 19.2

Question 1
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 1
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 2
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 2
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 3
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 3
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 4
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 4
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 5
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 5
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 6
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 6
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 7
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 7
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 8
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 8
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 9
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 9
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 10
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 10
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 11
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 11
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 12
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 12
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 13(a)

In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that

RN and RM trisect QS.

Solution 13(a)

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 13(b)

In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that

PMRN is a parallelogram.

Solution 13(b)

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 13(c)

In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that

MN bisects QS.

Solution 13(c)

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 14
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Solution 14
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals
Question 15(a)

In the given figure, PQRS is a parallelogram in which PA = AB = Prove that:

SA QB and SA = QB.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 15(a)

Construction:

Join BS and AQ.

Join diagonal QS.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 15(b)

In the given figure, PQRS is a parallelogram in which PA = AB = Prove that:

SAQB is a parallelogram.

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 15(b)

Construction:

Join BS and AQ.

Join diagonal QS.

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 16(a)

In the given figure, PQRS is a trapezium in which PQ SR and PS = QR. Prove that:

PSR = QRS and SPQ = RQP

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Solution 16(a)

Construction:

Draw SM PQ and RN PQ

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 17

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that:

  1. BC = BE.
  2. CE is the bisector of angle C and angle DEC is a right angle
Solution 17

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

Question 18

Prove that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus.

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Let ABCD be a quadrilateral, whose diagonals AC and BD bisect each other at right angle.

i.e. OA = OC, OB = OD

And, AOB = BOC = COD = AOD = 90°

To prove ABCD a rhombus, we need to prove ABCD is a parallelogram and all sides of ABCD are equal.

Now, in ΔAOD and DCOD

OA = OC  (Diagonal bisects each other)

AOD = COD (Each 90°)

OD = OD   (common)

∴ΔAOD ≅ΔCOD  (By SAS congruence rule)

AD = CD  ….(i)

Similarly, we can prove that

AD = AB and CD = BC ….(ii)

From equations (i) and (ii), we can say that

AB = BC = CD = AD

Since opposite sides of quadrilateral ABCD are equal, so, we can say that ABCD is a parallelogram.

Since all sides of a parallelogram ABCD are equal, so, we can say that ABCD is a rhombus.

Question 19

Prove that the diagonals of a kite intersect each other at right angles.

Solution 19

Consider ABCD is a kite.

Then, AB = AD and BC = DC

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Question 20

Prove that the diagonals of a square are equal and perpendicular to each other.

Solution 20

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals

 

Frank Solutions Icse Class 9 Mathematics Chapter - Quadrilaterals