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Dear Student,
I have solved Q.9. Kindly post separate queries in different threads
ABCD is a parallelogram and BD is one of its diagonals.
As we know the opposite side of parallelograms are equal,
∴AB = CD and AD= BC
In ΔABD and ΔCDB,
AB= CD( given)
AD= BC (given)
BD= BD (common side)
∴ ΔABD ΔCDB ( By SSS congruency rule)
Similarly, we can prove join AC and prove that ΔABC ΔCDA.
Hence, the diagonal of a parallelogram divides it into 2 congruent triangles.