Class 9 Maths chapter Quadrilaterals Important Questions

9 CBSE Maths chapter  9th Quadrilaterals

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.
10. Show that each angle of a rectangle is a right angle.
11. Show that the diagonal of a rhombus are perpendicular to each other.
12. Show that the bisectors of the angles of a parallelogram form a rectangle.
13. 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
14. 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
15.If the diagonal of a parallelogram are equal, then show that it is a rectangle.
16. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
17. Show that the diagonals of a square are equal and bisect each other at right angles.
17. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
18. 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.
19.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.
20.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.
21.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.
22.Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
23.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.
24, Show that diagonal of isosceless triangle are equal.
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