consider a paralleogram ABCD where ths side AB a and BC b a

consider a paralleogram ABCD, where ths side AB= a and BC = b are given and have equal length ||a|| = ||b||

find the diagonal AC and BD

2) determin the angle between AC and BD (hint use : a)

Solution

A paralleogram ABCD, where the side AB= a and BC = b are given and have equal length i.e. ||a|| = ||b||, is a rhombus. Then:

1. At the best we can determine a relation between the sum of the square of the lengths of the diagonals. Since the diagonals of a rhombus bisect each other are perpendicular to each other, hence, by the Pythagores theorem, we have ||(1/2) AC||²+||(1/2) BD||² = a² or, ||AC||² +||BD||²= 4a².

2. The diagonals of a rhombus are perpendicular to each other. Hence they intersect at right angles (90⁰). This means that they are perpendicular. Thus, the angle between AC and BD is 90⁰.