Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 1:
Homework

Problem H1

Draw five quadrilaterals, each on its own piece of patty paper. Use one quadrilateral for each construction below.

 a. Construct the eight medians of the first quadrilateral. (There will be two medians at each vertex.) b. Construct the four midlines of the second quadrilateral. c. Construct the four angle bisectors of the third quadrilateral. d. Construct the four perpendicular bisectors of the sides of the fourth quadrilateral. e. Construct four altitudes in the fifth quadrilateral -- one from each vertex.

 Problem H2 Try Problem H1 with a few different quadrilaterals. Don't just use "special" cases, like squares and rectangles. Record any observations about the constructions above. How is the situation different from what you saw with triangles?

 Problem H3 Imagine a square casting a shadow on a flat floor or wall. Can the shadow be non-square? Non-rectangular? That is, can the angles in the shadow ever vary from 90°?

 Problem H4 Which of these shapes could cast a square shadow, and which could not? Explain how you decided.