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Class 9 FRANK Solutions 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.

Quadrilaterals Exercise Ex. 19.1

Solution 1(a)

Solution 1(b)

Solution 1(c)

Solution 1(d)

Solution 1(e)

Solution 2

Solution 3

 

 

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

 

Construction: Join PR.

 

 

Solution 14

Solution 15

Quadrilaterals Exercise Ex. 19.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 13(a)

 

 

Solution 13(b)

 

 

Solution 13(c)

 

 

Solution 12

Solution 14

Solution 15(a)

Construction:

Join BS and AQ.

Join diagonal QS.

 

 

Solution 15(b)

Construction:

Join BS and AQ.

Join diagonal QS.

 

 

Solution 16(a)

Construction:

Draw SM PQ and RN PQ

 

Solution 17

 

 

Solution 18

 

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.

Solution 19

Consider ABCD is a kite.

Then, AB = AD and BC = DC

 

 

 

Solution 20

 

 

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