2. If the diagonals of a parallelogram are equal, then show that it is a rectangle. 3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then 4. Show that the diagonals of a square are equal and bisect each other at right ang is a rhombus. 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at D angles, then it is a square. 6. Diagonal AC of a parallelogram ABCD bisects ZA (see Fig. 8.19). Show that (1) it bisects 2 C also. (i) ABCD is a rhombus. B 7. ABCD is a rhombus. Show that diagonal AC bisects Z A as well as < C and diagonal BD bisects ZB as well as ZD. 8. ABCD is a rectangle in which diagonal AC bisects LA as well as ( Show (1) ABCD is a square (in Fig. 8.19
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