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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.