Shortest Distance, Perp Bis, and Angle Bis Conjectures

Move point C above until the length of CD is the shortest. Notice the angle measure that results. Then, complete the conjecture and add to your vocabulary list. Shortest Distance Conjecture: The shortest distance from a point to a line is measured along the ___________________________ segment from the point to the line.

Line CM the perpendicular bisector of segment AB. Move point C along the perpendicular bisector. Then, complete the following conjecture and add to your vocabulary list. Perpendicular Bisector Conjecture: If a point is on the perpendicular bisector of a segment, then it is ___________________________ to the endpoints of the line segment.

Ray FK is the angle bisector of angle LFN. Segments KL and KN are the shortest distances from point K to the sides of the angle. Move point K around. Then, complete the following conjecture and put in your vocabulary. Angle Bisector Conjecture: If a point is on the angle bisector of a segment, then it is ______________________ to the sides of the angle.

Point C represents your house on the road (line AB). Construct (with compass and straightedge) the shortest possible driveway from your house to the road. What conjecture applies to this problem?

Cassidy and Chelsey are roommates and want to find a place to live that is equidistant to their respective jobs. Construct (with compass and straightedge) a line that shows all possible places they can live that would be the same distance to their workplaces. What conjecture applies here?

Construct a ray that shows places the goalie should stand. What conjecture applies to this scenario?