P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle.
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.
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.
In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.
Data on some of the public facilities are collected as part of the Census. Discuss with your
teacher when and how the Census is conducted.
A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.
Are the above public facilities shared equally by all the people in your area? Elaborate.
A diagonal of a parallelogram bisects one of its angle. Prove that it will bisect its opposite angle also.
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