![]() ![]() The easy way to construct a perpendicular bisector #PQ# to segment #AB# is pictured below. Here the centers of these circles are the endpoints of a given segment #AB# and their radiuses must be the same. The only condition is for these circles is the existence two points of intersection, #P# and #Q#. For this the radius can be any, as long as it's greater than half of the length of #AB#. The simple method is to choose it to be equal to the length of #AB#. ![]() Wednesday 9/30/98 Topic: Similar Triangles and Pythagorean Theorem Criteria for similarity of triangles will be used to prove several.Monday, 9/28/98 Topic: Congruent Triangles SAS, SSS and ASA criteria for triangle congruence.So, we have proven that #M# is a modpoint of #AB# and #PM_|_AB#.Math 444 Syllabus and Topic Outline Math 444 Syllabus and Topic Outline #=>/_AMP=/_BMP# as angles of congruent triangles lying across congruent sides #AP# and #BP#=> AM=BM# as sides of congruent triangles lying across congruent angles #/_APM=/_BPM#=> Delta APM = Delta BPM# by side-angle-side theorem #=>/_APQ=/_BPQ# as angles of congruent triangles lying across congruent sides #AQ# and #BQ#Delta APQ = Delta BPQ# - by side-side-side theorem #AP=BP=AQ=BQ# - each is a radius, which we have chosen What's more interesting is to prove that this construction delivers the perpendicular bisector.Īssume that #M# is an intersection of #AB# and #PQ#. Math 487 Lab #1 Wednesday 9/28/98 Introduction to Geometer's Sketchpad Students will be introduced to the Sketchpad software by workingĬhapter 2 of GTC will also be used, so bringĮmail List Everyone should be on the email list.Results, including the Pythagorean Theorem. Getting email from the list this week you are on otherwise, ANSWERS TO GSP5 CONSTRUCTING PERPENDICULAR BISECTORS SOFTWARE Getting Acquainted with Sketchpad (Part 1).This class will meet in the Thomson Computer Lab. Topic: Tangents and Chords of Circles This lab will work through Chapter 2 of GTC. To traces of points and lines in Sketchpad. Reading GTC (Geometry Through the Circle), Chapter 2.īack to Top. Monday, 10/5/98 Topic: Similarity and Parallels (2) Theorem of Thales as simplest case of similarity.Reading B&B, Chapter 4 Bix, Chapter 1, Section 0. Wednesday 10/7/98 Topic: Division Ratios Signed (Positive and Negative) Ratios are key tools in understanding. ![]() Math 487 Lab #2 Wednesday 10/7/98 Topic: Perpendicular Bisectors, Circles and Distance This lab will work through Chapter 3 of GTC.Ģ1-38.Īssignment 3 Due Midpoint Quadrilaterals, cubes and others.The main goal is to see theĬonnection between the perpendicular bisector of a segment and the locus of points Perpendicular bisectors and the constuction of the circumcircle. Reading GTC (Geometry Through the Circle),Chapter 3. Topic: Carpenter's Construction This lab will work through GTC Chapter 4. This is applied to an introduction to moreĪn important application is the construction of the tangent lines to a given circle This uses someĭetailed geometry of the right triangle, especially the fact that the midpoint Of the vertex of right angles ABC for fixed A and B is a circle. Monday, 10/12/98 Topic: Two More Concurrence Theorems.Reading GTC (Geometry Through the Circle), Chapter 4. Where the perpendicular bisectors of the legs interesect is the Proof of perpendicular bisector concurrence for a general triangle.) Midpoint of the hypotenuse, one needs more than equal distances, oneĪlso needs to show the point is on the hypotenuse. Proof of concurrence of medians of a triangle with connection to.Midpoint parallelogram of a quadrilateral. Proof of concurrence of altitudes of triangle ABC the key is toĬonstruct a larger triangle A'B'C' so that ABC is the midpoint.Parallel to the sides of ABC and distances are determined by finding Wednesday 10/14/98 Topic: Line Symmetry and Reflection with a Mirror Using the Reflectview Mirror to reflect objects and investigate symmetry.Some points include how to construct a perpendicularīisector with this mirror. What are the lines of symmetry of familiarįigures such as an equilateral triangle (3), a rhombus (2), a rectangle (2),Ī general paralellogram (0), a circle (infinitely many), a line segment (2),Ī line (infinitely many), and the X-figure made of two intersecting lines ANSWERS TO GSP5 CONSTRUCTING PERPENDICULAR BISECTORS HOW TO ANSWERS TO GSP5 CONSTRUCTING PERPENDICULAR BISECTORS SOFTWARE.ANSWERS TO GSP5 CONSTRUCTING PERPENDICULAR BISECTORS HOW TO. ![]()
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