By the end of the lesson, students will be able to draw perpendicular bisectors, angle bisectors, and understand locus of points using only a ruler and compass. The document then provides examples of drawing various loci including the perpendicular bisector of a segment as the set of points equidistant from the endpoints, the locus of points a certain distance from a given point or line, and how the perpendicular bisectors of a triangle's sides and bisectors of its angles intersect at the circumcenter and incentre, respectively.

1. By the end of the lesson you will be able to:
• Draw the perpendicular bisector of a segment
and bisectors of angles using ruler and compasses.
• Understand, identify and draw locus of points.
1

2. Mark all the points that are at the same distance from A
and B.
A B
Mediatriz 2.ggb
Conclusion:
The set of all the points equidistant from the end points of a
line segment is the perpendicular bisector of the segment.
2

3. How to draw the perpendicular bisector of a segment
A B
The locus of a point is the path traced out by the point as it moves .
3

4. The locus of a point is the path traced out by the point as it moves .
The locus of points which are equidistant from two
given points A and B is the perpendicular bisector of
the segment AB
A B
A locus is a set of points which fit a condition.
4

5. Draw the locus of points which are closer to A than to B.
A B
5

6. Draw the locus of points which are at 3 cm from P
=
Locus.ggb
Draw all the points which are at 3 cm from P
•P
The locus of the points whose distance to a fixed point P is
constant is the circumference of centre P.
6

7. Draw the locus of points that are 3 cm from line AB.
A B
7

8. Locus of points that are 3 cm from line AB.
A B
http://math.nie.edu.sg/bwjyeo/it/MathsOnline_EM/geosketch/jsps/IT4EMLoci1LineAns.html
8

9. Draw the locus of points which are 3 cm from AB
A B
9

10. Draw the locus of points which are 3 cm from AB
A B
10

11. Construct the bisector of the angle:
http://www.mathopenref.com/constbisectangle.html
11

12. The points on the bisector of the angle are at the same distance
from both arms of the angle.
The locus of all the points which are equidistant
from the sides of an angle is the bisector of the
angle
12

13. Draw the locus of points which are closer to side OP than to side OL.
P
O
L
13

14. Draw the locus of the points Draw the locus of the
which are 3 cm or less from points which are more than
a point O. 3 cm from O.
. O
14

15. Draw the perpendicular bisectors of all the sides
in the triangle
The perpendicular bisectors of the sides of a triangle meet at a
point called the circumcentre.
The circumcentre is at the same distance from each vertex.
The circumcentre is the centre of a circunference that passes
through the three vertices.
15

16. Draw all the bisectors of the angles of the triangle
The bisectors of the angles of a triangle meet at a point called the incentre.
The incentre is at the same distance from each side of the triangle.
The incentre is the centre of a circunference that touches the three sides of the triangle.
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17. Attachments
Locus.ppt
Worksheet LOCI.doc
Circumscribed.ppt
Perpendicular bisector.ggb
Mediatriz 2.ggb
Circumference Locus.ggb