# Shortest Distance, Perp Bis, and Angle Bis Conjectures

## Shortest Distance Conjecture Investigation

## Shortest Distance Conjecture

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.

## Perpendicular and Angle Bisectors Investigations

## Perpendicular Bisector Conjecture

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.

## Angle Bisector Conjecture

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.

## Driveway Problem

## Driveway Problem

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?

## Roommates Problem

## Roommates 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?

## Soccer Goalie Problem

## Soccer Goalie Problem

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