Segments AB and CD meet at point O. Prove that OC = OD if AC = AO = BO = BD.
| September 26, 2021 | education
1) Since in these triangles AOC and BOD are equal on two sides, AC = AO = OB = BD. For the equality of two triangles, you also need the equality of the angles between equal sides.
2) Consider the angles of these triangles. In the AOC triangle, the angles at the base of the AO are equal: <ACO = <AOC.
3) In the triangle ВDО, the angles at the base ОD, <BOD = <ВDО, since ОВ = ВD by condition. And since the angles <DОВ = <СОА, as vertical, then the angles <САО = <ОВD. Means. and triangles ACO and OBD are equal.
4) Hence, the sides OC = OD, as sides against equal angles.
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