2.10 Activity
Split a segment into 2 equal pieces by constructing the perpendicular bisector.
Follow the steps below to construct a perpendicular bisector.
1) Use "Compass" to construct a circle with radius AB centered at A.
2) Use "Compass" to construct a circle with radius AB centered at B.
3) Use "Intersect" to mark the points of intersection of the two circles.
4) Use "Line" to draw a line through those two points.
5) Use "Intersect" to mark the point where the line intersects segment AB.
*Optional - Measure your 2 segments to verify that they are equal.
Split segment AB into 2 equal pieces.
Below are the steps for constructing a perpendicular bisector. Follow these steps again to split segment AB into 2 equal parts. THEN, split those two segments into 2 equal parts.
*Hint: You will do 3 perpendicular bisector constructions here.
1) Use "Compass" to construct a circle with radius AB centered at A.
2) Use "Compass" to construct a circle with radius AB centered at B.
3) Use "Intersect" to mark the points of intersection of the two circles.
4) Use "Line" to draw a line through those two points.
5) Use "Intersect" to mark the point where the line intersects segment AB.
*Optional - Measure your 2 segments to verify that they are equal.
Split segment AB into 4 equal pieces.
How can we split a segment into 3 equal pieces using dilations?!
Follow the steps below to split a segment into 3 (or any number of) pieces.
1) Construct a line parallel to the segment (ALREADY DONE FOR YOU).
2) Mark point C so that it is to the left of point A (ALREADY DONE FOR YOU).
3) From point C use "Compass" to mark off equal segments (ALREADY DONE FOR YOU).
*You can use "Compass" to add more points here if you like. They must all have radius set to CD.
**Important: The last point on line CD must be to the right of point B.
4) Use "Ray" to construct ray CA.
5) Use "Ray" to contruct ray FB. (or from whatever your rightmost point is)
6) Use "Intersect" to mark the point where these rays intersect. This is the center of dilation.
7) Use "Ray" to construct rays from the remaining points on line CD to the center of dilation.
8) Use "Intersect" to mark the points where each ray intersects segment AB.
Your segment AB has now been split into 3 or more equal pieces. Use "Distance or length" to verify that they are equal.