Ενώνοντας τα μέσα των πλευρών ενός τετραπλεύρου
Στην παρακάτω εφαρμογή βλέπετε ένα τετράπλευρο και μπορείτε να μετακινήσετε τις κορυφές του όπου εσείς θέλετε.
Παίξε με την εφαρμογή μερικά λεπτά και μετά απάντησε τις ερωτήσεις που ακολουθούν.
Questions:
1) How do you know the smaller white points are midpoints? Explain.
2) Notice how the midpoints of the sides of this quadrilateral form vertices of yet another quadrilateral.
How would you classify this quadrilateral? That is, what would be the most specific name you'd give
this quadrilateral?
3) What observation(s), in the applet above, prompted you to give the classification you did for (2)?
Explain fully why/how this applet informally suggests that your answer to (2) is correct.
4) Formally prove that the midpoints of the sides of any quadrilateral always form vertices
of this type of specific quadrilateral. Prove this using the format of a 2-column or paragraph proof.
(If you need a hint getting started, refer to this worksheet.)
5) Use coordinate geometry to formally prove your response to (2) is true.
(Hint: Place one vertex of this quadrilateral at (0,0). Place another vertex at (2a, 0).)