Lecture
Theorem (properties of a rhombus).
Diagonal rhombus intersect at right angles. Diagonal rhombus are the bisectors of its angles.
Evidence.
Let ABCD be a given diamond. Diagonal diamonds intersect at point O.
By the property of the parallelogram AO = OC, then BO is the median Δ ABC. And since the triangle ABC is isosceles, by the properties of the median of an isosceles triangle conducted to the base, BO is also a height and a bisector. Hence the straight line BO ⊥ AC and ∠ ABO = CBO. The theorem is proved.
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Planometry
Terms: Planometry