Question

Геометрия 8 класс: из вершины тупого угла ромба проведён перпендикуляр к его стороне делящий эту сторону пополам. найти углы ромба.

Answer 1

В ромбе АВСД угол-В=углуД=60градусов
уголА=углуС=180-60=120град

Answer 2

Finding the Angles of a Rhombus

To find the angles of a rhombus when a perpendicular is drawn from a vertex of the obtuse angle to the midpoint of one of its sides, we can use the properties of a rhombus.

1. Properties of a Rhombus: - A rhombus is a type of parallelogram with all sides having equal length. - The diagonals of a rhombus bisect each other at right angles.

2. Solution: - When a perpendicular is drawn from a vertex of the obtuse angle to the midpoint of one of its sides, it creates two right-angled triangles within the rhombus. - Since the diagonals of a rhombus bisect each other at right angles, the obtuse angle is split into two equal acute angles.

3. Conclusion: - Therefore, the angles of the rhombus are equal and each measures half of the obtuse angle.

Based on the properties of a rhombus and the construction described, the angles of the rhombus are split into two equal acute angles from the obtuse angle. This means that each angle of the rhombus measures half of the obtuse angle.