The segments AC and BD intersect at point O. AO = OC, BO = OD. When segments AB and CD

| April 24, 2021 | education

The segments AC and BD intersect at point O. AO = OC, BO = OD. When segments AB and CD are drawn, triangles BAO and OCD are formed. Prove that ∆ BAO = ∆ OCD

To prove the equality of two triangles, we use the first sign of equality of triangles: if two sides and the angle between them of one triangle are equal to two sides and the angle between them of another triangle, then these triangles are equal.

In our problem: one side of the AO of the first triangle is equal to the side of the OC — of the other. The second side of the BO is equal to OD.

When two lines intersect, two pairs of equal vertical angles are formed. In our case: angle AOB = angle COD.

We have two sides and the angle between them of one triangle, which correspond to the two sides and the angle between them of another triangle.

Therefore, the triangles BAO and OCD are equal.



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