- Quadrilateral
- |
- Parallelogram
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- Trapezium
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- Rhombus
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- Rectangle
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- Square
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- Mid-point Theorem for Triangles
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- How to solve the angle Problem in Quadilateral
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- Additional Topics

Given below are the

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

Q1 If the diagonals of parallelogram are equal, then show that it is a rectangle.

Q2. Show that if the diagonals of the quadrilateral bisect each other at right angles, then it is a rhombus.

Q3. Show that the diagonals of a square are equal and bisect each other at right angles.

Q4. Show that if the diagonals of the quadrilateral are equal and bisect each other at night angles, then it is a square.

Q5. ABCD is a rectangle in which diagonal AC bisect <A as well as <C. Show that-

- ABCD is a square
- Diagonal BD bisects <B a well as <D.

Q7. 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.

Q8. 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.

Q9. Show that the line segments joining the mid- point of the opposite sides of a quadrilateral bisect each other.

Q10. 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 = ½ AB.

Q12. In a parallelogram ABCD, <D = 135, determine the angles measures of <A and <B.

Q13. ABCD is a parallelogram in which <A = 70. Compute <B, <C and <D.

Q14. ABCD is a parallelogram in which <DAB = 75 and <DBC = 60. Compute <CDB and <ADB.

Q15. 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.

Q17. 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.

Q18. 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.

Q19. 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.

Q20. 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.

Q21. 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.

Q23. 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.

Q24. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Q25. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.

Q26. 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.

Q27. A diagonal of a rectangle is inclined to one side of a rectangle at 25

Q28. 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.

Q29. Show that the quadrilateral formed by joining the mid- points of adjacent sides of rectangle is a rhombus.

Q30. Show that the diagonals of a square are equal and bisect each other at right angles.

Q31. Prove that the quadrilateral formed (if possible) by the internal angular bisectors of any quadrilateral is cyclic.

Q32. 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.

Class 9 Maths Home page Class 9 Science Home page

- NCERT Exemplar Problems: Solutions Mathematics Class 9
- IIT Foundation & Olympiad Explorer - Class 9 (Maths)
- Mathematics - Class 9 RD Sharma
- NCERT Solutions - Mathematics for Class IX
- Olympiad Excellence Guide for Mathematics (Class-9)
- MTG Foundation Course for JEE/Olympiads - Class 9 Maths
- Mathematics foundation course for Boards /JEE/PETs/ NTSE