For a point, give a construction of a line so the portion intercepted by the segments of a given angle are bisected at the point.
check out the many references on constructing a perpendicular bisector of a segment. Your problem does not specify a perpendicular bisector, but that is the easiest way to find the midpoint of a line segment.
Draw your angle and a line traversing its sides. Then just construct the perpendicular bisector of that segment.
Thank you.
To construct a line such that the portion intercepted by the segments of a given angle is bisected at a point, follow these steps:
1. Start by drawing the given angle with its vertex at a point on a sheet of paper.
2. Take a compass and set its width to any arbitrary length. Make an arc from the vertex of the angle, intersecting both sides of the angle.
3. Without changing the compass width, draw two more arcs, one intersecting each side of the angle, with their centers at the points where the previous arc intersected the angle's sides.
4. Label these points of intersection as A and B.
5. Take a ruler and draw a line segment connecting points A and B.
6. Bisect this line segment by constructing a perpendicular bisector. To do this, use a compass to measure the width of the line segment, then create arcs above and below the line segment.
7. Connect the points of intersection of these arcs to form a line.
8. This line will intersect the segments of the angle, bisecting them at the point where it intersects the angle.
Following these steps will result in a line that intercepts the segments of the given angle and bisects them at the desired point.