Segments AB and CD intersect at point O. CO = OD, ⦟ BCD = ⦟ CDA. Prove that AD = CB.
| June 28, 2021 | education
Given:
segments AB and CD,
point O – the point of intersection of segments AB and CD,
CO = OD,
angle ВСD = angle СDА.
Prove that AD = CB.
Evidence:
Consider triangle AOD and triangle COB. Angle AOD = angle of COB, as these angles are vertical angles. Angle ВСD = angle СDА and СО = ОD according to the problem statement. Therefore, triangle AOD = triangle COD along the side and two adjacent corners. Then AD = BC. Q.E.D.
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