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
Solutions for Chapter 8: Quadrilaterals
Below listed, you can find solutions for Chapter 8 of CBSE NCERT for Class 9 Maths.
NCERT solutions for Class 9 Maths Chapter 8 Quadrilaterals Exercise 8.1 [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.]
NCERT solutions for Class 9 Maths Chapter 8 Quadrilaterals Exercise 8.2 [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 parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig.) Show that the line segments AF and EC trisect the diagonal BD
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
Solutions for Chapter 8: Quadrilaterals
NCERT solutions for Class 9 Maths chapter 8 - Quadrilaterals
Shaalaa.com has the CBSE Mathematics Class 9 Maths CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 9 Maths CBSE 8 (Quadrilaterals) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Class 9 Maths chapter 8 Quadrilaterals are Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles, Angle Sum Property of a Quadrilateral, Types of Quadrilaterals, Another Condition for a Quadrilateral to Be a Parallelogram, Theorem of Midpoints of Two Sides of a Triangle, Property: The Opposite Sides of a Parallelogram Are of Equal Length., Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles., Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram., Property: The Opposite Angles of a Parallelogram Are of Equal Measure., Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram., Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection), Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram.
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