Chapter 2: Polynomials
Chapter 3: Coordinate Geometry
Chapter 4: Linear Equations in two Variables
Chapter 5: Introduction to Euclid's 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 Area and Volumes
Chapter 14: Statistics
Chapter 15: Probability
NCERT Mathematics Class 9
Chapter 8 : Quadrilaterals
Pages 146 - 147
The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Show that the diagonals of a square are equal and bisect each other at right angles.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that
(i) It bisects ∠C also,
(ii) ABCD is a rhombus.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:-
(i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see the given figure). Show that:
(i) ΔAPD ≅ ΔCQB
(ii) AP = CQ
(iii) ΔAQB ≅ ΔCPD
(iv) AQ = CP
(v) APCQ is a parallelogram
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ
In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ΔABC ≅ ΔDEF.
ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ΔABC ≅ ΔBAD
(iv) diagonal AC = diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]
Pages 150 - 151
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see the given figure). AC is a diagonal. Show that:
(i) SR || AC and SR = 1/2AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
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.
ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.
In a parallelogrFind the values of k for each of the following quadratic equations, so that they have two equal roots. 2x2 + kx + 3 = 0
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = 1/2AB
NCERT Mathematics Class 9
Textbook solutions for Class 9
NCERT solutions for Class 9 Mathematics chapter 8 - Quadrilaterals
NCERT solutions for Class 9 Maths chapter 8 (Quadrilaterals) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 9 solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Class 9 Mathematics chapter 8 Quadrilaterals are The Mid-point Theorem, Another Condition for a Quadrilateral to Be a Parallelogram, Properties of a Parallelogram, Types of Quadrilaterals, Angle Sum Property of a Quadrilateral, Concept of Quadrilaterals.
Using NCERT Class 9 solutions Quadrilaterals exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.
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