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The arcs must intersect because you need a point to use with the point of the angle's vertex to make the line that intersects the angle.

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Q: When constructing an angle bisector why must the arcs intersect?
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How do you draw a perpendicular bisector?

Drawing perpendicular bisector for a line:Place the sharp end of a pair of compasses at one end of the line, and open it to just over half of the line. Draw an arc which must intersect the line in the position described. Then put the sharp end at the other of the line and, keeping the compassing at the same length, draw another arc which intersects the first one twice and also the line. Then draw a straight line through the two places where the arcs intersect. This line is the perpendicular bisector. Drawing perpendicular bisector of angle:Places the sharp end of the compass at the point of the angle and, after having opened it arbitraily wide, draw an arc which intersects the two lines meeting to form the angle each once in the said position. Then remove the compass and, always keeping it opened at the SAME length, place the sharp end at each of the two places where the previous arc cuts each of the two lines meeting to form the angle. In this position with the described length, draw a small arc at each of the said places, which should cross each other. Draw a straight line from the point of the angle to this crossing. This should be the bisector of the angle.


The measure of a tangent-tangent angle is half the difference of the measures of the intercepted arcs?

True


How do you find midpoint of a segment?

Take a compass, extend it about 3/4 of the length of the segment. Then from one end of the segment, draw a 180 degree arc. From the other end draw another arc. Connect the points where the arcs intersect. Where the line intersects with the segment is the midpoint of the segment. That is how you bisect a segment to find the midpoint - geometrically.


How do you construct 32 degree angle using ruler and compass?

Well, honey, you start by drawing a line with your ruler. Then, you put the point of your compass on one end of the line and draw an arc. Next, you put the point of your compass on where the arc intersects the line and draw another arc. Where those arcs meet is your 32-degree angle. Voila!


How do you draw a spherical triangle where the sum of the angles is 190 degrees?

You could draw two arcs from the North pole to the equator, with a 10 degree separation. The two arcs and the equator would form a 190 degree spherical triangle.