CBSE Important Questions

CBSE Guess > Papers > Important Questions > Class IX > 2011 > Maths > Mathematics By Mr. Amit Kumar Jha

CBSE CLASS IX

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Quadrilaterals

Section A

Prove that followings:

  1. A diagonal of a parallelogram divides it into two congruent triangles.
  2. In a parallelogram, opposite sides and angle are equal.
  3. If each pair of opposite sides of quadrilateral is equal, then it is a parallelogram.
  4. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
  5. The diagonals of a parallelogram bisect each other.
  6. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
  7. A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.
  8. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.
  9. The line segment joining the mid- points of the two sides of a triangle is parallel to the third side.

Section B

  1. Show that each angle of a rectangle is a right angle.
  2. Show that the diagonal of a rhombus are perpendicular to each other.
  3. ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD||AB. Show that
    (i) angle DAC=angle BCA and
    (ii) ABCD is a parallelogram (||gm).

  4. Show that the bisectors of the angles of a parallelogram form a rectangle.
  5. ABCD is a parallelogram (||gm) in which P and Q are mid-points of opposite side AB and CD. If AQ intersects DP at S and BQ intersects CO at R, show that (i) APCQ is ||gm
    (ii)DPBQ is ||gm
    (iii) PSQR is ||gm

  6. In Triangle ABC, D, E and Fare respectively the mid points of sides AB, BC and CA. Show that triangle ABC is divided into four congruent triangle by joining D, E and F

Section C

  1. If the diagonal of a parallelogram are equal, then show that it is a rectangle.
  2. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
  3. Show that the diagonals of a square are equal and bisect each other at right angles.
  4. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
  5. In a parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ. Show that

    (ii) AP=CQ

    (iv) AQ=CP
    (v) APCQ is a parallelogram.

  6. In Δ ABC and Δ DEF, AB=DE, AB||DE, BC=EF and BC||EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that:
    (i) Quadrilateral ABCD is a parallelogram.
    (ii) Quadrilateral BEFC is a parallelogram.
    (iii) AD||CF and AD=CF
    (iv) Quadrilaterals ACFD is a parallelogram
    (v) AC=DF
    (vi) Δ ABC Δ DEF.
  7. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that:
    (i) SR||AC and SR =1/2 AC
    (ii) PQ=SR
    (iii) PQRS is a parallelogram.
  8. ABCD is a rhombus and P, Q, R and S are the mid- point of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
  9. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
  10. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
  11. ABC is a triangle right angle at C. A line through the mid-points M of hypotenuse AM and parallel to BC intersects AC at D. Show that
    (i) D is the mid –point of AC
    (ii) MD ┴ AC
    (iii) CM=MA=1/2 AB.

 

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Submitted By Amit Kumar Jha
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