When You Learn Your Scales And Your Geometry...
- Kendyl Wade
For this applet, the multi-colored polygons are the original figures and the brown polygons are the secondary image.
Figure A 1. Drag point B. What do the two polygons have in common? What is different about them? 2. Click checkbox A for the lengths of sides A’B’ and AB. Write a conjecture about the relationship between these two lengths. 3. Drag point A and compare the lengths of A’B’ and AB again. Does your conjecture still hold? If not, adjust your conjecture so that it does hold. 4. Click checkbox B for the lengths of sides B’C’ and BC, C’D’ and CD, D’E’ and DE, and E’A’ and EA. Do all of these pairs of sides maintain your conjecture? Why might this be true? 5. Do you think your conjecture will hold for the area of the two polygons? Use your conjecture to calculate the area of Poly2, and then click checkbox C to check your answer. What did you notice? 6. Drag one of the points on Poly1. What do you notice about the area of the two polygons? What is their relationship? Write a conjecture about the relationship between the areas. 7. What connections can you make between your conjecture in #3 and your conjecture in #6? Figure B 8. Click checkbox D for the lengths of the sides of Poly3 and Poly4. What is the relationship between the lengths? 9. Drag one of the points of Poly3. Does this relationship hold? 10. Click checkbox E for the area of Poly3 and Poly4. What is the relationship between Poly3 and Poly4? 11. Does the connection you made in #7 hold for Figure B? If not, adjust your connection to make a general conjecture. Figure C 12. Drag one of the points on Poly5. What is the relationship between Poly5 and Poly6? How is this relationship different from the relationships in Figure A and B? 13. Click checkbox F for the area of the polygons. What is the relationship between the areas? Does your conjecture from #11 hold for Figure C? If not, adjust it so that it holds for Figures A, B, and C.