• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4

NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.

  • Areas of Parallelograms and Triangles Class 9 Ex 9.1
  • Areas of Parallelograms and Triangles Class 9 Ex 9.2
  • Areas of Parallelograms and Triangles Class 9 Ex 9.3
  • Areas of Parallelograms and Triangles Class 9 Ex 9.4
Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 9
Chapter Name Areas of Parallelograms and Triangles
Exercise  Ex 9.4
Number of Questions Solved 8
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4

Ex 9.4 Class 9 Maths Question 1.
Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.
Solution.
We have a parallelogram ABCD and rectangle ABEF such that
ar (parallelogram ABCD) = ar (rectangle ABEF)
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.1

Ex 9.4 Class 9 Maths Question 2.
In figure, D and E are two points on BC such that BD = DE = EC. Show that
ar (Δ ABD) = ar (Δ ADE) = ar (Δ  AEC).
Can you now answer the question that you have left in the ‘Introduction’ of this chapter, whether the field of Budhia has been actually ‘ divided into three parts of equal area?
[Remark: Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD, ADE and AEC of equal areas. In the same way, by dividing BC into n equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide Δ ABC into n triangles of equal areas.]
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.2
Solution.
Given : ABC is a triangle, D and E are two points on BC, such that BD = DE – EC.
To prove :     ar (Δ  ABD) = ar (Δ ADE) = ar (Δ AEC)
Proof: Let AO be the perpendicular to BC.
We know that,
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.3

Ex 9.4 Class 9 Maths Question 3.
In the figure, ABCD, DCFE and ABFE are parallelograms.Show that ar (Δ ADE) = ar (Δ BCF).
Solution.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.4
Given : ABCD, DCFE and ABFE are parallelograms.
To prove : ar (Δ ADE) = ar (Δ BCE)
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.5

Ex 9.4 Class 9 Maths Question 4.
In the figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, then show that ar (Δ BPO = ar (Δ DPQ.) [Hint: Join AC]
Solution.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.6

Ex 9.4 Class 9 Maths Question 5.
In the figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, then show that
(i) ar (Δ BDE) = \(\cfrac { 1 }{ 4 } \)ar (Δ ABO)
(ii) ar (Δ BDE) = \(1-\cfrac { 1 }{ 2 } \)ar (Δ BAE)
(iii) ar (Δ ABC) = 2 ar (Δ BEO
(iv) ar (Δ BFE) = ar (Δ AFD)
(v) ar (Δ BFE) = 2 ar (Δ FED)
(vi) ar (Δ FED) = \(1-\cfrac { 1 }{ 8 } \) ar (Δ AFC).
[Hint: Join EC and AD. Show that BE || AC and DE || AB, etc.]
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.7
Solution.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.8
Join AD and EC
Let x be the side of equilateral Δ ABC.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.9
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.10
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.11
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.12
Ex 9.4 Class 9 Maths Question 6.
Diagonals AC and BD of a quadrilateral ABCD intersect each other at P.
Show that  ar (ΔAPB) x ar (Δ CPD)
= ar (Δ APD) x ar (Δ BPC). [Hint: From A and C, draw perpendiculars to BD].
Solution.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.13
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.14

Ex 9.4 Class 9 Maths Question 7.
P and Q are respectively the mid-points of sides AB and BC of a Δ ABC and R is the mid-point of AP, show that
(i) ar (Δ PRQ) = \(\cfrac { 1 }{ 4 } \) ar (Δ ARC)
(ii) ar (Δ RQC = \(\cfrac { 3 }{ 8 } \)ar (Δ ABC)
(iii) ar (Δ PBQ) = ar (Δ ARC).
Solution.
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.15
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.16
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.17
Ex 9.4 Class 9 Maths Question 8.
In the figure, ABC is a right angled triangle, right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB, respectively, Line segment AX ⊥DE meets BC at Y. Show that
(i) Δ MBC ≅ Δ ABD
(ii) ar (BYXD) = 2 ar (Δ MBC)
(iii) ar (BYXD) = ar (Δ BMN)
(iv) ΔFCB ≅  AACE
(v) ar (CYXE) = 2 ar (Δ FCB)
(vi) ar (CYXE) = ar (ACFG)
(vii) ar (BCED) = ar (ABMN) + ar (ACFG).
[Note: Result (vii) is the famous Theorem of Pythagoras. You shall term a similar proof by this Theuonern is class X.]
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.18
Solution.
Given: ABC is a right  angled triangle in which ∠A = 90°. BCED, ACFG and ABMN are squares. Line segment AX ⊥ DE meets BC at Y
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.19
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.20
NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4.21

We hope the NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4 help you. If you have any query regarding NCERT Solutions for Class 9 Maths 9 Areas of Parallelograms and Triangles Ex 9.4, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • Algebra Coefficient of term Workedout problems
  • factor theorem applications Find factor of polynomial
  • CBSE Class 9 maths solutions Triangles Ex 7 1 NCERT Class 9 maths solutions
  • CBSE Class 9 Maths solutions Heron’s Formula Ex 12 2 NCERT Class 9 Maths solutions
  • CBSE Class 9 Maths solutions Heron’s Formula Ex 12 1 NCERT Class 9 Maths solutions
  • CBSE Class 9 maths solutions Introduction to Euclid’s Geometry Ex 5 1
  • CBSE Class 9 maths solutions Lines and Angles Ex 6 3 NCERT Class 9 maths solutions
  • factor theorem examples factor theorem questions
  • factoring cubic polynomials Factorise by splitting middle term and factor theorem Ex 2.4
  • factoring quadratic polynomial by splitting the middle term
  • Factoring Trinomials by Using the Punnett Square Ex 2 4
  • Factorise cubic polynomial factoring polynomials using algebraic identities Ex 2 5
  • Factorise polynomials Factorizing using algebraic identities Ex 2 5
  • Factorize perfect square trinomials Algebraic identities Ex 2 5
  • Factor theorem Find unknown coefficient in polynomial given factor of polynomial

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
cbse ncert
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions