2.Show that the diagonals of a rhombus divide it intofour congruent tr

1.	2.Show that the diagonals of a rhombus divide it intofour congruent triangles.
Answer» Let the rhombus be ABCD and let therediameters intersect each other at O.Since,in a Rhombus all sides are equal. Therefore AB=AD and since ABCD isrhombus therefore its diagonals bisect each other. So,AO=DOandAO=AO(common)ThereforeΔABO=~ΔADOSimilarly,ΔABO=~ΔBCO Similarly,ΔBCO=~ΔDCO Therefore, ΔABO=~ΔBCO=~ΔCDO=~ΔADO

2.Show that the diagonals of a rhombus divide it intofour congruent triangles.

Answer»

Let the rhombus be ABCD and let therediameters intersect each other at O.Since,in a Rhombus all sides are equal.

Therefore AB=AD and since ABCD isrhombus therefore its diagonals bisect each other.

So,AO=DOandAO=AO(common)ThereforeΔABO=~ΔADOSimilarly,ΔABO=~ΔBCO

Similarly,ΔBCO=~ΔDCO

Therefore, ΔABO=~ΔBCO=~ΔCDO=~ΔADO