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

From points A and B, lying on one side of the straight line, perpendiculars AC and BD are drawn to this straight line; angle BAC = 117 ° a) Find the angle ABD b) Prove that lines AB and CD intersect.

1) Because AC and BD are perpendicular to a straight line, then they are parallel. <BAC and <ABD – internal one-sided angles with parallel straight lines AC and BD and secant AB. The sum of the inner one-sided angles is 180 degrees.

<BAC + <ABD = 180;

<ABD = 180 – <BAC;

<ABD = 180 – 117 = 63

Answer. 63 degrees.

2) Suppose that lines AB and CD do not intersect, that is, that they are parallel. Then <BAC and <ACD are internal one-sided with parallel AB and CD and secant AC.

<BAC + <ACD = 180;

<BAC = 117; <ACD = 90; 117 + 90 = 207, and should be equal to 180 – we got a contradiction. This means that our assumption that the lines do not intersect is incorrect.

So AB and CD – intersect.