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Balbharati solutions for Class 9 Geometry chapter 5 - Quadrilaterals

Balbharati Class 9 Mathematics 2 Geometry

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Balbharati Balbharati Class 9 Mathematics 2 Geometry

Balbharati Class 9 Mathematics 2 Geometry - Shaalaa.com

Chapter 5: Quadrilaterals

Practice Set 5.1Practice Set 5.2Practice Set 5.3Practice Set 5.4Practice Set 5.5Problem Set 5

Chapter 5: Quadrilaterals Exercise Practice Set 5.1 solutions [Page 62]

Practice Set 5.1 | Q 1 | Page 62

Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ = 135°  then what is the measure of  ∠XWZ and  ∠YZW ? 
If l(OY)= 5 cm then l(WY)= ?

Practice Set 5.1 | Q 2 | Page 62

In a parallelogram ABCD, If ∠A =(3x + 2)° , ∠B = (2x - 32)° then find the value of x and then find the measures of  ∠C and  ∠D.  

Practice Set 5.1 | Q 3 | Page 62

Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.

Practice Set 5.1 | Q 4 | Page 62

If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.

Practice Set 5.1 | Q 5 | Page 62

Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that
`square`ABCD is a rhombus. 

Practice Set 5.1 | Q 6 | Page 62

In the given figure, `square` PQRS and `square` ABCR are two parallelograms. If  ∠P =110°  then find the measures of  all angles of `square` ABCR.

Practice Set 5.1 | Q 7 | Page 62

In the given figure, `square` ABCD is a parallelogram. Point E is on the ray AB such that BE = AB then prove that line ED bisects seg BC at point F.

Chapter 5: Quadrilaterals Exercise Practice Set 5.2 solutions [Page 67]

Practice Set 5.2 | Q 1 | Page 67

`square` ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove `square` APCQ is a parallelogram.

Practice Set 5.2 | Q 2 | Page 67

Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Practice Set 5.2 | Q 3 | Page 67

In the given figure, G is the point of concurrence of medians of Δ DEF. Take point H on ray DG such that D-G-H and DG = GH, then prove that `square` GEHF is a parallelogram.

Practice Set 5.2 | Q 4 | Page 67

Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.(shown in the given figure)

Practice Set 5.2 | Q 5 | Page 67

In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square` PQRS is a parallelogram.

Chapter 5: Quadrilaterals Exercise Practice Set 5.3 solutions [Page 69]

Practice Set 5.3 | Q 1 | Page 69

Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35°  then find ∠ACB

Practice Set 5.3 | Q 2 | Page 69

In a rhombus PQRS if PQ = 7.5 then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.

Practice Set 5.3 | Q 3 | Page 69

Diagonals of a square IJKL intersects at point M, Find the measures of ∠ IMJ, ∠ JIK and ∠ LJK .

Practice Set 5.3 | Q 4 | Page 69

Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Practice Set 5.3 | Q 5.1 | Page 69

State with reason whether the following statement is ‘true’ or ‘false’.

Every parallelogram is a rhombus.

Practice Set 5.3 | Q 5.2 | Page 69

State with reason whether the following statement is  ‘true’ or ‘false’.

Every rhombus is a rectangle.

Practice Set 5.3 | Q 5.3 | Page 69

State with Reason Whether the Following Statement is ‘True’ Or ‘False’.

Every rectangle is a parallelogram.

Practice Set 5.3 | Q 5.4 | Page 69

State with reason whether the following statement is  ‘true’ or ‘false’.

Every squre is a rectangle.

Practice Set 5.3 | Q 5.5 | Page 69

State with reason whether the following statement is  ‘true’ or ‘false’.

Every square is a rhombus.

Practice Set 5.3 | Q 5.6 | Page 69

State with reason whether the following statement is ‘true’ or ‘false’.

Every parallelogram is a rectangle.

Chapter 5: Quadrilaterals Exercise Practice Set 5.4 solutions [Page 71]

Practice Set 5.4 | Q 1 | Page 71

In `square` IJKL,  side IJ || side KL ∠I =180° ∠K = 53° then find the measure of ∠J and  ∠L.

Practice Set 5.4 | Q 2 | Page 71

In `square` ABCD , side  BC || side AD, side AB ≅ side DC  If ∠A = 72°  then find the measure of  ∠ B, and  ∠ D.

Practice Set 5.4 | Q 3 | Page 71

In `square`ABCD , side BC < side AD in following figure .
side BC || side AD and if side BA ≅ side CD then prove that ∠ ABC ≅ ∠ DCB.

Chapter 5: Quadrilaterals Exercise Practice Set 5.5 solutions [Page 73]

Practice Set 5.5 | Q 1 | Page 73

In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of Δ ABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

Practice Set 5.5 | Q 2 | Page 73

In the given figure, `square` PQRS and `square` MNRL are rectangles. If point M is the midpoint of side PR then prove that,

(i) SL = LR,    (ii) LN = `1/2`SQ

Practice Set 5.5 | Q 3 | Page 73

In the given figure, Δ ABC is an equilateral traingle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that Δ FED is an equilateral traingle.

Practice Set 5.5 | Q 4 | Page 73

In the given figure, seg PD is a median of Δ PQR. Point T is the mid point of seg PD. Produced QT intersects PR at M. Show that `(PM)/(PR) = 1/3`
[Hint: DN || QM]

Chapter 5: Quadrilaterals Exercise Problem Set 5 solutions [Pages 73 - 74]

Problem Set 5 | Q 1.1 | Page 73

Choose the correct alternative answer and fill in the blank.

If all pairs of adjacent sides of a quadrilateral are congruent then it is called ....

  • rectangle 

  • parallelogram

  •  trapezium 

  • rhombus

Problem Set 5 | Q 1.2 | Page 73

Choose the correct alternative answer and fill in the blank.

If the diagonal of a square is `12 sqrt 2` cm then the perimeter of square is ......

  • 24 cm

  • `24sqrt2` cm

  • 48 cm

  • `48 sqrt2` cm

Problem Set 5 | Q 1.3 | Page 73

Choose the correct alternative answer and fill in the blank.

 If opposite angles of a rhombus are (2x)° and (3x - 40)° then value of x is ...

  • 100°

  • 80°

  • 160°

  • 40°

Problem Set 5 | Q 2 | Page 74

Adjacent sides of a rectangle are 7 cm and 24 cm. Find the length of its diagonal.

Problem Set 5 | Q 3 | Page 74

If diagonal of a square is 13 cm then find its side.

Problem Set 5 | Q 4 | Page 74

Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.

Problem Set 5 | Q 5 | Page 74

Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

Problem Set 5 | Q 6 | Page 74

Diagonals of a rectangle PQRS are intersecting in point M. If  ∠QMR = 50° find the measure of ∠MPS.

Problem Set 5 | Q 7 | Page 74

In the adjacent Figure ,

if seg AB || seg PQ , seg AB ≅ seg PQ,  seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.

Problem Set 5 | Q 8 | Page 74

In the given Figure, `square` ABCD is a trapezium. AB || DC .Points P and Q are midpoints of seg AD and seg BC respectively.
Then prove that, PQ || AB and PQ = `1/2 (AB + DC)`.

Problem Set 5 | Q 9 | Page 74

In the adjacent figure, `square` ABCD is a trapezium AB || DC . Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB .

Chapter 5: Quadrilaterals

Practice Set 5.1Practice Set 5.2Practice Set 5.3Practice Set 5.4Practice Set 5.5Problem Set 5

Balbharati Balbharati Class 9 Mathematics 2 Geometry

Balbharati Class 9 Mathematics 2 Geometry - Shaalaa.com

Balbharati solutions for Class 9 Geometry chapter 5 - Quadrilaterals

Balbharati solutions for Class 9 chapter 5 (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 Maharashtra State Board Balbharati Class 9 Mathematics 2 Geometry 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. Balbharati 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 Geometry chapter 5 Quadrilaterals are The Mid-point Theorem, Concept of Trapezium, Properties of Rectangle, Properties of Square, Properties of Rhombus, Tests for parallelogram, Parallelogram, Concept of Quadrilaterals.

Using Balbharati 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 Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 9 prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 5 Quadrilaterals Class 9 extra questions for and can use Shaalaa.com to keep it handy for your exam preparation

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