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Answer this question 9. Prove that a diagonal of a parallelogram divides it into two congruent triangles. 10. In the figure, ABCD is a rhombus. Find the values of x and y. Also, find all the angles of rhombus. 500 x o c 11. ABCD is a parallelogram whose diagonals intersect each other at O. Through O, a line segment PQ is drawn as shown in the figure. Show that OP = OQ. c (2015-432VKV4, 30GOX8T) Four Marks Questions 12. In the figure given below, ABCD is a rhombus whose side AB is produced to points P and Q such that AP = AB = BQ. PD and QC are produced to meet at a point R. Show that ZPRQ = 900 c side: figm

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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.

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