Segments AC and BD intersect at point O. Prove the equality of triangles BCO and DAO

| February 26, 2021 | education

Segments AC and BD intersect at point O. Prove the equality of triangles BCO and DAO if it is known that both BCO = DAO and AO = CO.

Given: AC intersects BD – at point O; AO = CO; angle BCO = angle DAO.

Prove: triangle AOD = triangle BOC.

Since AC and BD intersect at point O – by condition, we will draw segments BC and AD. We get that the BC segment will be parallel to the AD segment.

Then the angle CBO = angle ADO – as crossing at the secant BD and parallel lines BC and AD.

Angle BOC = Angle AOD – as vertical angles.

Since they are vertical, the angles BOA and COD are also equal and vertical. Therefore, the segment BO = AO = CO = DO.

Thus, all 3 angles of these triangles are equal, two sides, and hence the third, are equal, and we get that the AOD triangles themselves and the BOC triangle are equal in three sides and three corners.



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