Question

4) Diagonals of a parallelogram intersect each other at point
0. If PO = 5, QO = 12 and PQ = 13 then,show that
quadrilateral PQRS is a rhombus.​

Answer 1

Consider triangle AOB,

AO = 5 cm, BO = 12 cm

AO2 + BO2 = 52 + 122

= 25 + 144

= 169

= 132

As, AO2 + BO2 = AB2

Hence, using converse of Pt=ythagoras theorem triangle AOB is right angle triangle.

So, diagonals are perpendicular to each other. Hence, ABCD is a rhombus.

Answer 2

Step-by-step explanation:

first we congruent all the small triangles then we find pq = qr =Sr = ps then by using the measurements we can easily prove that it is a rhombus

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