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Teacher Notes

CONCEPT 1 -- Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

### (3) Bisect a segment

 TEACHER NOTE -- In diagram (c) the points A, C, B & D form a rhombus because the same radii has been used. It is the property of a rhombus that the diagonals bisect each other that helps us find our point M correctly.

### (4) Bisect an angle

 TEACHER NOTE -- In diagram (e) the points A, C, D & B form a rhombus because the same radii has been used. It is the property of a rhombus that the diagonals are angle bisectors that helps us correctly get the angle bisector.

### (5) Construct the perpendicular bisector of a line segment

 TEACHER NOTE -- In diagram (c) the points A, C, B & D form a rhombus because the same radii has been used. It is the property of a rhombus that the diagonals are perpendicular and diagonals bisect each other that helps us find the perpendicular bisector.

### (6) Construct a line perpendicular to a given line through a point NOT on the line.

not

 TEACHER NOTE -- In diagram (d) the points A, C, B & D form a rhombus because the same radii has been used. It is the property of a rhombus that the diagonals are perpendicular that helps us create the perpendicular line.

### (7) Construct a line perpendicular to a given segment through a point on the line.

 TEACHER NOTE -- In diagram (d) the points C, D, B & E form a rhombus because the same radii has been used. It is the property of a rhombus that the diagonals are perpendicular that helps us create the perpendicular line.

### (8) Construct a line parallel to a given line through a point not on the line.

 TEACHER NOTE -- There are lots of ways to do this construction. I have basically copied an angle. Another way to look at it is that I have created a parallelogram in diagram (d) with points C, A, E & D. It is a parallelogram because opposite sides are congruent.