Question

You are given the steps for constructing the bisector of an angle using a compass and a straightedge. Arrange the steps in the correct sequence. Place the compass needle on the vertex of the given angle. Name the vertex point A. Move the compass needle to D. If required, adjust the compass width at this point. Draw an arc within the mouth, or opening, of the angle. Without changing the width of the compass, move its needle to point E and draw another arc that crosses the arc drawn from D. Draw an arc intersecting both rays of the angle. Mark and label the points of intersection D and E. Mark the point of intersection of the arcs centered at D and E. Label the point F. Draw a straight line from vertex A passing through point F. Ray A F bisects angle B A C. Set the compass to any convenient width.

Answer 1

To bisect an angle using a compass and straightedge:

1. Place the compass at the vertex, draw arcs intersecting, and connect the intersection with the vertex.

Step-by-step explanation:

The steps outlined above describe a geometric construction method for bisecting an angle. Using only a compass and straightedge, this process ensures the accurate division of the given angle into two equal parts. The key is to create intersecting arcs centered at distinct points (D and E) and then draw a line through the vertex (A) and the intersection point (F) to achieve the angle bisector.

This construction technique relies on the principles of Euclidean geometry, emphasizing the use of arcs and straight lines to create precise geometric constructions. By following these steps, one can geometrically construct an angle bisector, a fundamental concept in geometry and trigonometry.

These instructions provide a clear and concise guide, allowing anyone familiar with basic geometric tools to bisect an angle accurately. The method is practical, adhering to the principles of classical geometry and serving as a valuable skill in geometric constructions.