In rhombus ABCD, angle A is acute. From point B, the heights BK and BL

In rhombus ABCD, angle A is acute. From point B, the heights BK and BL are lowered to the sides AD and CD, respectively. Prove that triangles ABK and BCL are equal.

In a rhombus, the opposite angles are equal, then the angle BAD = BAK = BCD = BCL.

Triangles ABK and BCL are rectangular, since BK and BL, by condition, are the heights of the rhombus.

In a rhombus, all sides are equal, then AB = BC.

Then the triangles ABK and BCL are equal according to the third criterion of equality of right-angled triangles, according to the hypotenuse and acute angle, which was required to be proved.