Parallel lines a and b are intersected by two parallel secants AB and CD, where points A and C lie on line a
| August 10, 2021 | education
Parallel lines a and b are intersected by two parallel secants AB and CD, where points A and C lie on line a, and points B and D lie on line b Prove that AC = BD
By condition, parallel lines a and b are intersected by two parallel secants AB and CD, as a result of this, a quadrilateral ABCD is obtained, in which pairs of opposite sides AB and CD, AC and BD (belonging to straight lines a and b) are parallel, which means that the resulting quadrilateral ABCD is a parallelogram.
The opposite sides of the parallelogram are equal, so AC = BD, which is what was required to prove.
Answer: AC = BD.
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