AP Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Book Answers

AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 book solutions pdf online from this page.

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions PDF

Andhra Pradesh State Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks. These Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.

Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	9th
Subject	Maths
Chapters	Maths Chapter 8 Quadrilaterals Ex 8.4
Provider	Hsslive

How to download Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions Answers PDF Online?

Visit our website - Hsslive
Click on the Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Answers.
Look for your Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks PDF.
Now download or read the Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions for PDF Free.

AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals Exercise 8.4

Question 1.
ABC is a triangle. D is a point on AB such that AD = 14 AB and E is a point on AC such that AE = 14 AC. If DE = 2 cm find BC.
Solution:

Given that D and E are points on AB and AC.
Such that AD = 14 AB and AE = 14 AC
Let X, Y be midpoints of AB and AC.
Joint D, E and X, Y.
Now in ΔAXY; D, E are the midpoints of sides AX and AY.
∴ DE // XY and DE = 12 XY
⇒ 2 cm = 12 XY
⇒ XY = 2 x 2 = 4cm
Also in ΔABC; X, Y are the midpoints of AB and AC.
∴ XY//BC and XY = 12 BC
4 cm = 12 BC
⇒ BC = 4 x 2 = 8 cm

Question 2.
ABCD is a quadrilateral. E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

Solution:
Given that E, F, G and H are the midpoints of the sides of quad. ABCD.
In ΔABC; E, F are the midpoints of the sides AB and BC.
∴ EF//AC and EF = 12 AC
Also in ΔACD; HG // AC
and HG = 12 AC
∴ EF // HG and EF = HG
Now in □EFGH; EF = HG and EF // HG
∴ □EFGH is a parallelogram.

Question 3.
Show that the figure formed by joining the midpoints of sides of a rhom¬bus successively is a rectangle.
Solution:

Let □ABCD be a rhombus.
P, Q, R and S be the midpoints of sides of □ABCD
In ΔABC,
P, Q are the midpoints of AB and BC.
∴ PQ//AC and PQ = 12AC …………………..(1)
Also in ΔADC, ,
S, R are the midpoints of AD and CD.
∴ SR//AC and SR = 12AC ………………(2)
From (1) and (2);
PQ // SR and PQ = SR
Similarly QR // PS and QR = PS
∴ □PQRS is a parallelogram.
As the diagonals of a rhombus bisect at right angles.
∠AOB – 90°
∴ ∠P = ∠AOB = 90°
[opp. angles of //gm PYOX] Hence □PQRS is a rectangle as both pairs of opp. sides are equal and parallel, one angle being 90°.

Question 4.
In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.

Solution:
□ABCD is a parallelogram. E and F are the mid points of AB and CD.
∴ AE = 12AB and CF = 12CD
Thus AE = CF [∵ AB – CD]
Now in □AECF, AE = CF and AE ||CF
Thus □AECF is a parallelogram.
Now in ΔEQB and ΔFDP
EB = FD [Half of equal sides of a //gm]
∠EBQ = ∠FDP[alt. int.angles of EB//FD]
∠QEB = ∠PFD
[∵∠QED = ∠QCF = ∠PFD]
∴ ΔEQB ≅ ΔFPD [A.S.A. congruence]
∴ BQ = DP [CPCT] ……………… (1)
Now in ΔDQC; PF // QC and F is the midpoint of DC.
Hence P must be the midpoint of DQ
Thus DP = PQ …………….. (2)
From (1) and (2), DP = PQ = QB
Hence AF and CE trisect the diagonal BD.

Question 5.
Show that the line segments joining the mid points of the opposite sides of a quadrilateral and bisect each other.

Solution:
Let ABCD be a quadrilateral.
P, Q, R, S are the midpoints of sides of □ABCD.
Join (P, Q), (Q, R), (R, S) and (S, P).
In ΔABC; P, Q are the midpoints of AB and BC.
∴ PQ // AC and PQ = 12AC ………….(1)
Also from ΔADC
S, R are the midpoints of AD and CD
SR // AC and SR = 12 AC …………………(2)
∴ From (1) & (2)
PQ = SR and PQ //SR
∴ □PQRS is a parallelogram.
Now PR and QS are the diagonals of □ PQRS.
∴ PR and QS bisect each other.

Question 6.
ABC is a triangle right angled at’C’. A line through the midpoint M of hypotenuse AB and parallel to BC intersects AC at D. Show that
i) D is the midpoint of AC
ii) MD ⊥ AC
iii) CM = MA= 12AB

Solution:

Given that in ΔABC; ∠C = 90°
M is the midpoint of AB.
i) If ‘D’ is the midpoints of AC.
The proof is trivial.
Let us suppose D is not the mid point of AC.
Then there exists D’ such that AD’ = D’C
Then D’M is a line parallel to BC through M.
Also DM is a line parallel to BC through M.
There exist two lines parallel to same line through a point M.
This is a contradiction.
There exists only one line parallel to a given line through a point not on the line.
∴ D’ must coincides with D
∴ D is the midpoint of AC

ii) From (i) DM // BC
Thus ∠ADM = ∠ACB = 90°
[corresponding angles]
⇒ MD ⊥ AC

iii) In ∆ADM and ∆CDM
AD = CD [ ∵ D is midpoint from (i)]
∠ADM = ∠MDC (∵ 90° each)
DM = DM (Common side)
∴ ∆ADM = ∆CDM (SAS congruence)
⇒ CM = MA (CPCT)
CM = 12 AB (∵ M is the midpoint of AB)
∴ CM = MA = 12AB

AP Board Textbook Solutions PDF for Class 9th Telugu

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 exam preparation. The AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Books State Board syllabus with maximum efficiency.

FAQs Regarding Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Solutions

How to get AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook Answers??

Students can download the Andhra Pradesh Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.4 Answers PDF from the links provided above.

Can we get a Andhra Pradesh State Board Book PDF for all Classes?

Yes you can get Andhra Pradesh Board Text Book PDF for all classes using the links provided in the above article.

Important Terms

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4, AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks, Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4, Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook solutions, AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions, Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4, AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks, Andhra Pradesh State Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4, Andhra Pradesh State Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbook solutions, AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.4 Textbooks Solutions,

HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

Hsslive.co.in: Kerala Higher Secondary News, Plus Two Notes, Plus One Notes, Plus two study material, Higher Secondary Question Paper.

Thursday, July 14, 2022