3 Remember that for projective geometry, the dual of a statement is found by exchanging "point...
Part II. (4 pts) Given the axiom set for the Incidence Geometry as below: Undefined terms: point, line, on Definitions: 1. Two lines are intersecting if there is a point on both. 2. Two lines are parallel if they have no point in common. Axioms: I. Given any two distinct points, there is a unique line on both. II. Each line has at least two distinct points on it. III. There exist at least three points. IV. Not all points...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry, gcometry and D. for Neutral geometry for your identifications Example. A There is a triangle in which the sum of the measures of the interior angles is 180. a. The opposite sides of a parallelogram are congruent. b. Similar triangles may not be congruent. Lines perpendicular to the...
6. After doing a lesson on spherical geometry, you are planning to give your students the following statements. They will have to decide whether they are true or false and give explanations. Decide which are true and which are false and give your own explanation. a. Any two lines intersect at a unique point. b. A triangle can have three right angles. d. A triangle can have more than one obtuse angle. e. Through a point outside a line, one...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.] 5) Consider the following statements: I: If two triangles are congruent, then they have equal defect. II: If two triangles are similar, then they have...
11. We will prove the following statement by mathematical induction: Let 1,2tn be n2 2 distinct lines in the plane, no two of which are parallel Then all these lines have a point in common 1. For2 the statement is true, since any 2 nonparallel lines intersect 2. Let the statement hold forno, and let us have nno 1 inesn as in the statement. By the inductive hypothesis, all these lines but the last one (i.e. the nes 1,2.n-1) have...
Use WebGL to write a program that plays tic-tac-toe. The program should begin by drawing the game board (two vertical lines and two horizontal lines). When a player left-clicks on an open space, the program should draw an “X” in that square. When a player right-clicks on an open space, the program should draw an “O” in that square. The Xs must be different colors from the Os. Both of those colors must be different from the lines making the...
9 Geometry via calculus In this exercise you will see one way to use calculus to do grometry a) Here is one way to find the perpendicsler distance from a point to a line L (no caleulus yet) Let's say L has equation y-3r+2 and the point is (2.1) First, make a graph (picture) of the situation 2Now find an equation for the line AM through (2, 1) perpendicular to L (draw it first, of course). 3. Find the (coordinates...
Problem Statement A 5.0-4C point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-ųC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero? . Visual Representation • Draw a sketch of the charge distribution. Establish a coordinate system and show the locations of the charges. Identify the point P at which you want...
Problem Statement A 5.0-4C point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-ųC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero? . Visual Representation • Draw a sketch of the charge distribution. Establish a coordinate system and show the locations of the charges. Identify the point P at which you want...
Electric Fields Problem Statement A 5.0-uC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-uC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero? Visual Representation • Draw a sketch of the charge distribution. • Establish a coordinate system and show the locations of the charges. • Identify the point P at...