Explorations in Geometry
The sketch below shows an easy way to construct a rhombus.
1) Start with circle with Center at R.
2) Select two points on the circle, H and M,
3) Draw a circle centered at H passing through R
4) Draw another Circle centered at M and passing through R.
5) Create a point O at the intersection of the two circles.
6) Select Points R,H,O, & M and construct the polygon interior.
When you move H or M around the circle, the angles change, and you can adjust the length of the sides by adjusting the free point of the original circle.
Now that we have a Rhombus, hide the circles, and lets see what we can find out.
1) Construct the two diagonals of the Rhombus. What observations can you make about the diagonals. You should be able to make at least two conjectures.
2) Measure the area of the Rhombus and see if you can find a relationship between the diagonals and the area of the Rhombus.
3) Could you do a formal proof that this conjecture is true?
4) Write a brief paragraph about what you have discovered in this exploration.