Circles, Triangles and Kites oh my part 2 #MTBoS30 7 of 30

It’s Thursday.  Yesterday we talked about circles, chords, and kites.  Today we asked a very similar question:

Here’s the applet in action: (click the animation to open the applet)

 

This was similar to Wednesday.  We asked the same type of questions.  We saw similar relationships.  But it stood out enough for a unique post because a student enlightened me with  an observation I didn’t articulate.  When I repeated yesterday’s question, “What shapes do you see inside the triangle?” one student almost immediately replied, “Is that a kite?”  I had to look at it myself.  “Yeah, wow, that makes this conversation easy.”  My original plan was:

1. Focus on the Right angles/right triangles
2. Question if certain segments were congruent
3. Look at the reflection or congruence theorem that helps confirm the congruence
4. then finish off with some color coding.

Instead this students recognizes the 3 kites, then refers to her knowledge of the symmetry in kites.  Congruence, simplified.

To help students in transcribing the diagram onto paper to start doing some hand calculations we took a tip from a student in the first class:

1.  Lay Chromebook on its back
2. Increase brightness of screen, turn off some/all light in class
3. Trace

This was another good introduction and discussion with segments in circles.  We of course spent the last 1/3 or so of class practicing and becoming fluent with the skill with problems like:

 

 

At the end of the week we took a short quiz.  2 questions, same as these.  Today/tomorrow I’m going to try something new with how I grade them (thanks to some inspiration from Michael Fenton, Michael Pershan, and Ashli Black).  More on that later this weekend.

In the meantime, let’s keep rounding out this circle thing and see what other shenanigans we can come up with.