From points A and B lying on one side of the straight line, AC and BD are perpendicular to this straight

| July 11, 2021 | education

From points A and B lying on one side of the straight line, AC and BD are perpendicular to this straight line: angle BAC = 117 degrees a) find the angle ABD b) prove that lines AB and BD intersect.

Since, by condition, AC is perpendicular to the straight line CD and BD is perpendicular to CD, then AC is parallel to AD. And then the quadrilateral ABCD is a rectangular trapezoid with lateral sides CD and AB.

In a trapezoid, the sum of the angles at the lateral side is 180, then the angle ABD = (180 – BAC) = 180 – 117 = 63.

If two lines are perpendicular to the third line, then they are parallel and lie in the same plane.

Then points A, B, C, D lie in the same plane, point B is common for AB and BD, therefore they intersect, which was required to prove.

The sum of the angles BAC and ACD is not equal to 180, then the straight lines AB and CD are not parallel and also intersect.



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