## Important Questions for CBSE Class 9 Mathematics Chapter 2 Quadrilaterals

### IMPORTANT QUESTIONS

Question.1 Three angles of a quadrilateral are equal and the fourth angle is equal to 144 °. Find each of the equal angles of the quadrilateral.
Solution. Question.2 Two consecutive angles of a parallelogram are (x + 60) ° and (2x + 30) °. What special name can you give to this parallelogram ?
Solution. Question.3 If one angle of a parallelogram is 30 ° less than twice the smallest angle, then find the measure of each angle.
Solution. Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the  parallelogram. [CBSE-15-6DWMW5A]
Solution. Question.5 Solution. Question.6.If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral.
Solution. Rhombus.

Question.7 In quadrilateral PQRS, if âˆ P = 60 ° and âˆ Q : âˆ R : âˆ S = 2:3:7, then find the measure ofâˆ S.
Solution.  Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
Solution. Question.9 In the given figure, ABCD is a parallelogram. If âˆ B = 100 °, then find the value of âˆ A +âˆ C. Solution. Question.10 If the diagonals of a parallelogram are equal, then state its name.
Solution. Rectangle

Question.11 ONKA is a square with âˆ KON = 45 °. Determine âˆ KOA.
Solution. Question.12 PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.
Solution. Question.13 Solution. Question.14 Solution. Question. 15.If ABCD is a parallelogram, then what is the measure of âˆ A – âˆ C ?
Solution. âˆ A –âˆ C = 0 ° [opposite angles of parallelogram are equal]

Question.16 Prove that a diagonal of a parallelogram divide it into two congruent triangles.  [CBSE March 2012]
Solution. Given : A parallelogram ABCD and AC is its diagonal. Question.17 ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and  C on diagonal BD (see fig.). Show that :
(i) AAPB â‰… ACQD (ii) AP = CQ            [CBSE March 2012]
Solution. Question.18 Solution. Question.19 Solution. Question.20 Solution. Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle.  [CBSE March 2012]
Solution.  Question.22 ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. Show that AX\\CY. D x c
Solution. Question.23 Solution.  Question.24 ABCD is a quadrilateral in which the bisectors of âˆ A and  âˆ C meet DC produced at Y and BA produced at X respectively. Prove that : [CBSE-15-6DWMW5A]
Solution.  Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]
Solution. Question.26 D, E and F are respectively the mid-points of the sides AB, BC and CA of a triangle ABC. Prove that by joining these mid-points D, E and F, the triangles ABC is divided into four congruent triangles. [NCERT Exemplar Problem]
Solution. Question.27 Solution. Question.28 Solution. Question.29 Solution. Since line segment joining the mid-points of two sides of a triangle is half of the third side. Therefore, D and E are mid-points of BC and AC respectively. Question.30 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC ad D. Show that:
(i) D is the mid-point of AC
(ii) MD âŠ¥ AC
(iii) CM = MA = 1/2 AB. [CBSE March 2012]
Solution.  Question.31 Solution. Question.32 The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
Solution.  Question.33 Solution. Question.34 Solution.   Question.35 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC at D. Show that:
(i) D is the mid-point of AC
(ii) MDâŠ¥ AC
(iii) CM = MA =1/2  AB. [CBSE March 2012]
Solution. Question.36 Solution.  Question.37 ABCD is a rhombus. Show that diagonals AC bisects âˆ A as well as âˆ C and diagonal BD bisectsâˆ B as well as âˆ D
Solution. Question.38 Solution.  Question.39 Solution.  Here, in AABC, R and Q are the mid-points of AB and AC respectively. Question.40 Solution. Question.41 Solution.  Question. 42 ABCD is a parallelogram in which diagonal AC bisectsâˆ A as well as âˆ C. Show that ABCD is a rhombus. [CBSE-14-17DIG1U]
Solution. Question. 43 Solution.  Question.44 ABCD is a parallelogram. If the bisectors DP and CP of angles D and C meet at P on side AB, then show that P is the mid-point of side AB.  [CBSE-15-NS72LP7]
Solution. Value Based Questions (Solved)

Question.1 Solution. Question.2 Solution. Question.3 Solution.  