# Using a straightedge, draw several line segments of various lengths and then construct the perpendicular bisectors.Using a straightedge, draw several different angles of various measures and then...

Using a straightedge, draw several line segments of various lengths and then construct the perpendicular bisectors.

Using a straightedge, draw several different angles of various measures and then construct the angle bisectors

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### 1 Answer

You will, of course, have to draw these on your own. However, the following is the procedure:

(1) To construct a perpendicular bisector of a line segment.

Let `bar(AB)` be a line segment. Draw a circle centered at A with radius AB. Draw another circle centered at B with radius AB. These circles will intersect at two points; connect the points and the segment constructed is the perpendicular bisector of `bar(AB)` .

The two points are equidistant from A and B, so they lie on the perpendicular bisector.

(2) To construct the bisector of a given angle:

Draw `/_ABC` . Draw a circle centered at B of convenient radius. This circle intersects the ray BA at X, and the ray BC at Y.

Draw a circle centered at X and draw a circle centered at Y of the same radius. These circles will intersect at two points, one of which will be in the angle's interior. Connect this intersection to B and the resulting ray will be the angle bisector.