Question

1. what is the definition of a circle?
2. use straightedge and compass tools to construct the perpendicular bisector of segment ab
3. the diagram below was created with straightedge and compass moves...

write a statement about the relationships between lines a & b, lines a & c, and lines c & b

Explanation:

1. A circle is the set of all points in a plane that are at a given distance (radius) from a given point (center).
2. Steps for constructing perpendicular - bisector:

• Place the compass at point A and open it to a radius more than half the length of segment AB.
• Draw arcs above and below the segment.
• Without changing the compass width, place the compass at point B and draw similar arcs, intersecting the previous arcs at two points.
• Use the straightedge to draw a line through these two intersection points. This line is the perpendicular bisector of segment AB.

1. Analyzing the diagram, we can observe the following relationships:

• Lines A and B are parallel as they do not intersect and are equidistant from each other.
• Lines A and C are perpendicular as they intersect at a 90 - degree angle.
• Lines C and B are perpendicular as they intersect at a 90 - degree angle.

Answer:

1. A circle is the set of all points in a plane that are at a given distance (radius) from a given point (center).
2. Follow the steps above to construct the perpendicular bisector of segment AB.
3. Lines A and B are parallel; Lines A and C are perpendicular; Lines C and B are perpendicular.