Important Questions for CBSE Class 9 Mathematics Chapter 2 Quadrilaterals
The topics and sub-topics in Class 9 Maths Chapter 8 Quadrilaterals:
- Angle Sum Property Of A Quadrilateral
- Types Of Quadrilaterals
- Properties Of A Parallelogram
- Another Condition For A Quadrilateral To Be A Parallelogram
- The MidPoint Theorem
VERY SHORT ANSWER TYPE 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.
Question.2 Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?
More Resources for CBSE Class 9
- NCERT Solutions
- NCERT Solutions Class 9 Maths
- NCERT Solutions Class 9 Science
- NCERT Solutions Class 9 Social Science
- NCERT Solutions Class 9 English
- NCERT Solutions Class 9 Hindi
- NCERT Solutions Class 9 Sanskrit
- NCERT Solutions Class 9 IT
- RD Sharma Class 9 Solutions
Question.3 If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.
Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram. [CBSE-15-6DWMW5A]
Question.6.If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral.
Question.7 In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S.
Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
Question.9 In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.
Question.10 If the diagonals of a parallelogram are equal, then state its name.
Question.11 ONKA is a square with ∠KON = 45°. Determine ∠KOA.
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.
Question. 15.If ABCD is a parallelogram, then what is the measure of ∠A – ∠C ?
Solution. ∠A –∠C = 0° [opposite angles of parallelogram are equal]
SHORT ANSWER QUESTIONS TYPE-I
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 ≅ ACQD (ii) AP = CQ [CBSE March 2012]
Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]
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
SHORT ANSWER QUESTIONS TYPE-II
Question.24 ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that : [CBSE-15-6DWMW5A]
Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]
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. 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.
LONG ANSWER TYPE QUESTIONS
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 ⊥ AC
(iii) CM = MA = 1/2 AB. [CBSE March 2012]
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.
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) MD⊥ AC
(iii) CM = MA =1/2 AB. [CBSE March 2012]
Question.37 ABCD is a rhombus. Show that diagonals AC bisects ∠A as well as ∠C and diagonal BD bisects∠B as well as ∠D
Solution. Here, in AABC, R and Q are the mid-points of AB and AC respectively.
Question. 42 ABCD is a parallelogram in which diagonal AC bisects∠A as well as ∠C. Show that ABCD is a rhombus. [CBSE-14-17DIG1U]
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]
Value Based Questions (Solved)
NCERT Solutions for Class 9 Maths
- Chapter 1 Number systems
- Chapter 2 Polynomials
- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations in Two Variables
- Chapter 5 Introduction to Euclid Geometry
- Chapter 6 Lines and Angles
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heron’s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Class 9 Maths (Download PDF)