# Quadrangle ABCD-rhombus. The bisector BK of the angle ABD divides the side AD in half.

October 14, 2021 | education

| **Quadrangle ABCD-rhombus. The bisector BK of the angle ABD divides the side AD in half. Find: 1) the corners of the rhombus; 2) the smaller diagonal of the rhombus if its side is 10 cm.**

Since the bisector of the angle ABD we divide the side AD in half, then it is both the median and the height of the triangle ABD, and therefore AB = BD = AD = 10 cm, and the triangle ABD is equilateral

In an equilateral triangle, the internal angles are 60, then the angle BAD = ABD = ADB = 60.

The sum of the adjacent angles of the rhombus is 180, then the angle ABC = ADC = 180 – 60 = 120.

Answer: The angles of the rhombus are 60, 120, 60, 120, the smaller diagonal is 10 cm.

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