P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.
Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.
Talk to two workers (For example, construction workers, farm workers, factory workers, workers
at any shop) to find out if they are receiving the minimum wages laid down by law.
E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD. Prove that EF || AB and EF =1/2 (AB + CD).
[Hint: Join BE and produce it to meet CD produced at G.]
Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC.
ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that ∠A = ∠B and ∠C = ∠D.
P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram
Private educational institutions – schools, colleges, universities, technical and vocational training
institutes are coming up in our country in a big way. On the other hand, educational institutes run
by the government are becoming relatively less important. What do you think would be the
impact of this? Discuss.
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