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NCERT solutions for Class 9 Mathematics chapter 8 - Quadrilaterals

Mathematics Class 9

NCERT Mathematics Class 9 Ex. 8.10Ex. 8.20

Chapter 8: Quadrilaterals Exercise 8.10 solutions [Pages 146 - 147]

Ex. 8.10 | Q 1 | Page 146

The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.

Ex. 8.10 | Q 2 | Page 146

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Ex. 8.10 | Q 3 | Page 146

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Ex. 8.10 | Q 4 | Page 146

Show that the diagonals of a square are equal and bisect each other at right angles.

Ex. 8.10 | Q 5 | Page 146

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Ex. 8.10 | Q 6 | Page 146

Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that

(i) It bisects ∠C also,

(ii) ABCD is a rhombus. Ex. 8.10 | Q 7 | Page 146

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

Ex. 8.10 | Q 8 | Page 146

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.

Ex. 8.10 | Q 9 | Page 147

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 Ex. 8.10 | Q 10 | Page 147

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 Ex. 8.10 | Q 11 | Page 147

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. Ex. 8.10 | Q 12 | Page 147

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.] Chapter 8: Quadrilaterals Exercise 8.20 solutions [Pages 150 - 151]

Ex. 8.20 | Q 1 | Page 150

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. Ex. 8.20 | Q 2 | Page 150

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.

Ex. 8.20 | Q 3 | Page 150

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.

Ex. 8.20 | Q 4 | Page 150

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. Ex. 8.20 | Q 5 | Page 151

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 Ex. 8.20 | Q 6 | Page 151

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Ex. 8.20 | Q 7 | Page 151

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

Ex. 8.10Ex. 8.20

NCERT Mathematics 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 Class 9 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathematics chapter 8 Quadrilaterals are Concept of Quadrilaterals, Angle Sum Property of a Quadrilateral, Types of Quadrilaterals, Another Condition for a Quadrilateral to Be a Parallelogram, The Mid-point Theorem, Theorem : a Diagonal of a Parallelogram Divides It into Two Congruent Triangles, Theorem : a Diagonal of a Parallelogram Divides It into Two Congruent Triangles, In a Parallelogram, Opposite Sides Are Equal. Ab = Cd and Bc = Da, Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram., In a Parallelogram, Opposite Angles Are Equal., Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram., The Diagonals of a Parallelogram Bisect Each Other., Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram.

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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