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Intro to Constructions, Cong Segments, Cong Angles Copy.notebook October 02, 2014 CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 18:33 AM 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 18:36 AM Oct 27:42 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 18:39 AM 1 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook October 02, 2014 Why we learn about constructions 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. 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 18:43 AM Copying a line segment or Constructing Congruent Segments Oct 18:57 AM Copying a line segment or Constructing Congruent Segments Construct a copy of AB. Name your segment YZ. http://www.mathopenref.com/constcopysegment.html Oct 19:00 AM Oct 19:02 AM 2 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook Construct a copy of BC from the triangle. The congruent segment should have one endpoint at P. Name it PR. A October 02, 2014 Sum of line segments P http://www.mathopenref.com/constaddsegments.html C B Oct 19:06 AM Sum of line segments Oct 19:10 AM Construct a segment whose length is two times longer than the given segment. Construct a line segment whose length is equal to the sum of the given line segments. Oct 19:12 AM Oct 19:14 AM 3 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook October 02, 2014 Construct a line segment whose length is equal to the perimeter of the triangle below. s Oct 19:15 AM Oct 28:05 AM Copying an Angle or Constructing Congruent Angles Copying an Angle or Constructing Congruent Angles http://www.mathopenref.com/constcopyangle.html Construct an angle congruent to each of the angles below. N Z M X P Y Oct 19:17 AM Oct 19:19 AM 4 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook N October 02, 2014 Perpendicular bisector Friday, Oct. 3rd of a line segment M P N M http://www.mathopenref.com/constbisectline.html P Oct 28:19 AM Oct 19:36 AM Perpendicular bisector of a line segment Construct a segment that is half as long as the given line segment. Label this new segment JK. Draw the perpendicular bisector of the two line segments below. T R Oct 19:37 AM Oct 19:42 AM 5 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook October 02, 2014 Construct the perpendicular bisector of each side of triangle CAT below. What do you notice? Locate the midpoint, M, of EF. C F E A Oct 110:38 AM Construct the perpendicular bisector of each side of triangle DOG below. What do you notice? T Oct 19:43 AM Bisecting an Angle O http://www.mathopenref.com/constbisectangle.html D G Oct 110:03 AM Oct 110:08 AM 6 Intro to Constructions, Cong Segments, Cong Angles Copy.notebook Bisecting an Angle October 02, 2014 Construct the angle bisectors of each angle in triangle CAT. What do you notice? Bisect the two angles below. C N M Z X P Y A Oct 110:25 AM T Oct 110:28 AM Construct the angle bisectors of each angle in triangle DOG. What do you notice? O D G Oct 110:28 AM 7