As performed in the real lab:
Colored papers, a pair of scissors, gum.
1. Cut off quadrilateral ABCD (Fig a) of paper with prescribed dimensions.
2. Mark the mid-points P,Q,R and S of the side AB,BC,CD,and AD respectively by folding the sides.
3. Cut off the quadrilateral PQRS.
4. Now cut the quadrilateral PQRS along the diagonal PR into two triangles PQR and PSR.
5. Superimpose the ▲ PSR on ▲ PQR such that PS falls on QR.(Fig b)
6. The ▲PQR covers the ▲PSR exactly.
7. Thus SP=QR and RS=PQ
8. Therefore, quadrilateral PQRS is a parallelogram.
As performed in the simulator:
1. Form a quadrilateral ABCD by clicking on any 4 points in workbench area.
2. Mark mid-point of each line AB, BC, CD, AD as P, Q, R, S respectively.
3. Click and join midpoints of each side to form quadrilateral PQRS.
4. Click on quadrilateral PQRS to separate it from quadrilateral ABCD.
5. Click on point P and point R to draw diagonal PR.
6. Click on ▲PRQ and ▲ PRS respectively to fill them with distinct colors.
7. Click on "Cut Triangle" button to cut triangle PQR from quadrilateral PQRS.
8. ▲ PQR is draggable so you can drag it to any position in workbench area.
9. Rotate ▲ PQR using "Rotate Anti Clockwise" and "Rotate Clockwise" buttons.
10. Next step is to place triangle PQR over triangle PRS such that both of them overlap each other.
The ▲PQR overlaps ▲PSR.
Thus SP=QR and RS=PQ.
Therefore, quadrilateral PQRS is a parallelogram.
|1. What is the figure obtained by joining the mid-points of consecutive sides?|
|2. How is a mid-segment different from a median in a triangle?|
|3. What is the significance of the mid-segment in a triangle?|
|4. How can we prove that the mid-segment is parallel to the third side of a triangle?|
|5. Can the mid-segment be longer than the third side of a triangle?|