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Form 3 Mathematics
Mid-points of any quadrilateral
(Book 3B P.g 60 Supplementary Exercise 9 Question 4)
ABCD is a quadrilateral. P, Q, R and S are the mid-points of AB, BC, CD and DA respectively.
Drag the points B, C , D and observe PQRS. What kind of quadrilateral must PQRS be? Compare the areas of PQRS and ABCD. What can you say? Prove your conjectures.
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Further question If ABCD is a trapezium, what kind of quadrilateral is PQRS? |
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Further question If ABCD is a paralleologram, what kind of quadrilateral is PQRS? |
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Further question If ABCD is a rhombus, what kind of quadrilateral is PQRS? |
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Further question If ABCD is a rectangle, what kind of quadrilateral is PQRS? |
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Further question If ABCD is a square, what kind of quadrilateral is PQRS? |
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Further question PQRS is a quadrilateral, A is a free point, B, C, D and D' are points obtained by reflections. When will A and D' merge? Drag A, P, Q, R and S to investigate. If PQRS is fixed, what can you say about the length of AD' when A is dragged? Can you prove the result? Press the "Hint" button for the hints. |
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