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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.

### Solution 13

Construction: Join PR.

### 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 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)

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