Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Duality (projective geometry) wikipedia , lookup
Coxeter notation wikipedia , lookup
Tessellation wikipedia , lookup
Analytic geometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
History of geometry wikipedia , lookup
Euler angles wikipedia , lookup
Euclidean geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Homework 1 Geometry for Teachers, MTH 623, Fall 2014 Due date: Wednesday Sept 17th 1. Activity: (a) Draw and cut out an example of each type of convex quadrilateral. (b) Label and arrange the shapes to form a classification diagram for convex quadrilaterals. (c) Draw a Venn diagram for the classification of quadrilaterals. Submit your answer by gluing the shapes on a separate sheet of paper. 2. Let Q be a convex quadrilateral. Let P be the quadrilateral formed by joining the midpoints of adjacent sides of Q. Show that P is a parallelogram. 3. (a) Show that the diagonals of a parallelogram bisect each other. (b) Show that diagonals of a rhombus bisect the angles. (c) Draw an example of a paralellogram whose diagonals do not bisect the angles. 4. The distance p between two points P (x1 , y1 ) and Q(x2 , y2 ) is given by (x1 − x2 )2 + (y1 − y2 )2 . Use the distance formula in the |P Q| = plane to show the following: (a) Translations preserve distances i.e. If T : R2 → R2 is a translation then |P Q| = |T (P )T (Q)|. (b) Rotations about the origin preserve distances. (c) Reflections about the x-axis preserve distances.