CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1
Introduction to Constructions Constructions: The drawing of various shapes using only a pair of compasses and straightedge or ruler. No measurement of lengths or angles is allowed. ** You are not allowed to measure angles with a protractor, or measure lengths with a ruler. Oct 1 8:36 AM Compasses Compasses are a drawing instrument used for drawing circles and arcs. It has two legs, one with a point and the other with a pencil or lead. You can adjust the distance between the point and the pencil and that setting will remain until you change it. Try drawing some circles and arcs on your paper. Oct 1 8:39 AM 2
Straightedge 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 1 2 3 4 5 A straightedge is simply a guide for the pencil when drawing straight lines. In most cases you will use a ruler for this, since it is the most likely to be available, but you must not use the markings on the ruler during constructions. Oct 1 8:43 AM Why we learn about constructions The Greeks formulated much of what we think of as geometry over 2000 years ago. In particular, the mathematician Euclid documented it in his book titled "Elements", which is still regarded as an authoritative geometry reference. In that work, he uses these construction techniques extensively, and so they have become a part of the geometry field of study. They also provide insight into geometric concepts and give us tools to draw things when direct measurement is not appropriate. Oct 1 8:57 AM 3
Copying a line segment or Constructing Congruent Segments http://www.mathopenref.com/constcopysegment.html Oct 1 9:00 AM Construct a copy of AB. Copying a line segment or Constructing Congruent Segments Name your segment YZ. Oct 1 9:02 AM 4
Construct a copy of BC from the triangle. The congruent segment should have one endpoint at P. Name it PR. A P B C Oct 1 9:06 AM Sum of line segments http://www.mathopenref.com/constaddsegments.html Oct 1 9:10 AM 5
Sum of line segments Construct a line segment whose length is equal to the sum of the given line segments. Oct 1 9:12 AM Construct a segment whose length is two times longer than the given segment. Oct 1 9:14 AM 6
Oct 2 12:52 PM Construct a line segment whose length is equal to the perimeter of the triangle below. Oct 1 9:15 AM 7
s Oct 2 8:05 AM Copying an Angle or Constructing Congruent Angles http://www.mathopenref.com/constcopyangle.html Oct 1 9:17 AM 8
Copying an Angle or Constructing Congruent Angles Construct an angle congruent to each of the angles below. Z X N M P Y Oct 1 9:19 AM N M P N M P Oct 2 8:19 AM 9
Perpendicular bisector of a line segment Friday, Oct. 3rd http://www.mathopenref.com/constbisectline.html Oct 1 9:36 AM Perpendicular bisector of a line segment Draw the perpendicular bisector of the two line segments below. Oct 1 9:37 AM 10
Construct a segment that is half as long as the given line segment. Label this new segment JK. T R Oct 1 9:42 AM Locate the midpoint, M, of EF. F E Oct 1 10:38 AM 11
Construct the perpendicular bisector of each side of triangle CAT below. What do you notice? C A T Oct 1 9:43 AM C A T Oct 3 8:00 AM 12
Construct the perpendicular bisector of each side of triangle DOG below. What do you notice? O D G Oct 1 10:03 AM Bisecting an Angle http://www.mathopenref.com/constbisectangle.html Oct 1 10:08 AM 13
Bisecting an Angle Bisect the two angles below. N M Z X P Y Oct 1 10:25 AM Construct the angle bisectors of each angle in triangle CAT. What do you notice? C A T Oct 1 10:28 AM 14
Construct the angle bisectors of each angle in triangle DOG. What do you notice? O D G Oct 1 10:28 AM 15