Frames:

9. Wrap-up

Work through the following problems to check whether you can do everything that the outcomes at the beginning of this unit state.


Prove that in any parallelogram PQRS, the sum of the squares of the diagonals is equal to the sum of the squares of the sides, i.e.

PR2 + QS2 = PQ2 + QR2 + RS2 + SP2

You can confirm the result numerically in the applet.


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  1. Show that in the special case when PQRS is a rectangle, the result follows directly from the theorem of Pythagoras.
  2. Give a general geometric or trigonometric proof.
  3. Give a general coordinate proof.

Click here for a discussion:  


Given ΔABC with A(1, 2), B(3, 6) and C(5, -2), find the coordinates of:

  1. the orthocentre
  2. the centroid
  3. the circumcentre.
Also briefly summarise in words all the knowledge you needed to apply in solving the problem.

Find all possible values of k so that A(-1, 2), B(-10, 5), and C(-4, k) form a right-angled triangle.

Click here to see some discussion: