*construct*one using straightedge and compass.

What's the easiest way to construct a kite? Let's consider the properties of a kite -- in particular, the Kite Diagonal Theorem again:

The symmetry diagonal of a kite is the

*perpendicular bisector*of the other diagonal and bisects the two angles at the ends of the kite.

Aha, there's the perpendicular bisector! So to construct a kite, we can let any segment be one of the diagonals, and then we construct its perpendicular bisector to find the other (symmetry) diagonal. So after that we join the vertices of these two segments to form the sides of the kite.

If we were to do this using the U of Chicago's perpendicular bisector construction, the two diagonals end up bisecting each other and the kite becomes a rhombus. If one wants a non-rhombus kite, we can use the straightedge to extend the symmetry diagonal in one direction before joining the vertices.

In a classroom without compasses, we can use paper folding instead. We begin by drawing any triangle, and then reflect it with one of its sides as the mirror. The result will be a kite. Notice that in a pre-Common Core class, we use SSS to prove that the two halves of the kite are congruent -- that is, we use SSS to prove the kite properties. But in the U of Chicago's Chapter 7, we end up using the kite properties to prove SSS! There's that circularity again, that we must be careful to avoid.

This activity does not require me to scan and post an image, and so I won't.

So now I go into a week off from this blog, in order to align the school calendar on this blog with the Early Start calendar at the school where I will become a sub here in Southern California. (Note: With all the talk about the leadership at LAUSD in the news, let me state that the district where I'll be a sub is

*not*LAUSD. Also, I'm considering subbing in a second school district with a traditional Labor Day Start calendar, and so further adjustments may need to be made to may day counts.)

See you on Day 52, Monday, October 27th!

## No comments:

## Post a Comment