Given below are the Class 9 Maths Assignments for Quadrilaterals
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(d) Long answer questions
(e) Fill in the blanks
Question 1. If the diagonals of parallelogram are equal, then show that it is a rectangle.
Question 2.. Show that if the diagonals of the quadrilateral bisect each other at right angles, then it is a rhombus.
Question 3. Show that the diagonals of a square are equal and bisect each other at right angles.
Question 4. Show that if the diagonals of the quadrilateral are equal and bisect each other at night angles, then it is a square.
Question 5. ABCD is a rectangle in which diagonal AC bisect $\angle A$ as well as $\angle C$. Show that-
- ABCD is a square
- Diagonal BD bisects $\angle B$ a well as $\angle D$.
Question 6. l, m and n are three parallel lines intersected by transversal's p and q such that l, m and n cut off equal intercepts AB and BC on p. Show that l, m and n cut off equal intercepts DE and EF and q also.
Question 7. ABCD is a rhombus and P, Q, R and S are the mid points of sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
Question 8. ABCD is a rectangle and P, Q, R and S are mid points of the sides AB, BC, CD and DA respectively. Show that quadrilateral PQRS is a rhombus.
Question 9. Show that the line segments joining the mid- point of the opposite sides of a quadrilateral bisect each other.
Question 10. ABC is a triangle right angles at C. A line through the mid -point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
- D is mid- point of AC
- $CM = MA = \frac {1}{2} AB$
Question 11. In a quadrilateral ABCD, CO and DO are bisectors of $\angle C$ and $\angle D$ respectively. Prove that $\angle COD = \frac {1}{2} (\angle A + \angle B)$
Question 12. In a parallelogram ABCD, $\angle D = 135^0$, determine the angles measures of $\angle A \; and \; \angle B$
Question 13. ABCD is a parallelogram in which $\angle A = 70^0$. Compute $\angle B \; ,\; \angle C \;and \; \angle D$
Question 14. ABCD is a parallelogram in which $\angle DAB = 75^0$ and $\angle DBC = 60^0$. Compute $\angle CDB \; and \; \angle ADB$.
Question 15. ABCD is a parallelogram and x, y are the mid- points of sides AB and DC respectively. Show that in ABCD, AXCY is a parallelogram.
Question 16. The sides AB and CD of a parallelogram ABCD are bisected t E and F. Prove that EBFD is a parallelogram.
Question 17. ABCD is a square E, F, G and H are points on AB, BC, CD and DA respectively. Such hat AE = BF = CG = DH. Prove that EFGH is a square.
Question 18. ABCD is a rhombus, EABF is a straight line such that EA = AB = BF. Prove that ED and FC when produced meet at right angles.
Question 19. ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.
Question 20. ABCD is a parallelogram P is a point on AD such that AP = 1/3 AD and Q is a point on BC such that CQ = 1/3 BC. Prove that AQCP is a parallelogram.
Question 21. P is the mid- point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. Prove that
- AR = 2BC
- BR = 2BQ.
Question 22. ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the mid- points of the side, in order, is a rectangle.
Question 23. ABC is a triangle. D is a point on AB such that AD = ¼ AB and E is the point on A such that AE = ¼ AC. Prove that DE = ¼ BC.
Question 24. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Question 25. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.
Question 26. Show that the line segment joining the mid- point of any two sides of a triangle is parallel to third side and is equal to half of it.
Question 27. A diagonal of a rectangle is inclined to one side of a rectangle at $25^0$. Find the acute angles between the rectangle diagonals.
Question 28. P, Q, R and S are respectively the mid- point of sides AB, BC, CD and DA of a quadrilateral ABCD such that AC BD. Prove that PQRS is a square.
Question 29. Show that the quadrilateral formed by joining the mid- points of adjacent sides of rectangle is a rhombus.
Question 30. Show that the diagonals of a square are equal and bisect each other at right angles.
Question 31. Prove that the quadrilateral formed (if possible) by the internal angular bisectors of any quadrilateral is cyclic.
Question 32. PQ and RS are to equal and parallel line segments. Any point M not lying on PQ or RS is joined to Q and S and lines through P parallel to QM and through R parallel to SM meet at N. Prove that the line segments MN and PQ are equal and parallel to each other.
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Class 9 Maths
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