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AP Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Book Answers

AP Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Book Answers
AP Board Class 9 Maths Chapter 8 Quadrilaterals Ex 8.3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Book Answers


AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 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 8.3 books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 book solutions pdf online from this page.

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbooks Solutions PDF

Andhra Pradesh State Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 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 8.3 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 8.3 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 8.3 Textbooks. These Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 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 8.3 Books Solutions

Board AP Board
Materials Textbook Solutions/Guide
Format DOC/PDF
Class 9th
Subject Maths
Chapters Maths Chapter 8 Quadrilaterals Ex 8.3
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AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 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 8.3

Question 1.
The opposite angles of a parallelogram are (3x – 2)° and (x + 48)°. Find the measure of each angle of the parallelogram.
Solution:
Given that the opposite angles of a parallelogram are (3x – 2)° and (x + 48)°
Thus 3x – 2 = x + 48
(∵ opp. angles of a //gm are equal)
3x – x = 48 + 2
2x = 50
x = 502 = 25°
∴ The given angles are (3 x 25 – 2)° and (25 + 48) °
= (75 – 2)° and 73° = 73° and 73°
We know the consecutive angles are supplementary.
∴ The other two angles are (180°-73°) and (180°-73°)
= 107° and 107°
∴ The four angles are 73°, 107°, 73° and 107°.

Question 2.
Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.
Solution:
Let the smallest angle = x
Then its consecutive angle = 180 – x°
By problem (180 – x)° = (2x- 24)°
(∵ opp. angles are equal)
180 + 24 = 2x + x
3x = 204
x = 2043 = 68°
∴ The angles are
68°; (2 x 68 – 24)°; 68°; (2 x 68 – 24)°
= 68°, 112°, 68°, 112°

Question 3.
In the given figure ABCD is a paral-lelogram and E is the mid point of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB.

Solution:

Given that □ABCD is a parallelogram.
E is the midpoint of BC.
Let G be the midpoint of AD.
Join G, E.
Now in ΔAFD, GE is the line joining the midpoints G, E of two sides AD and FD.
∴GE // AF and GE = 12AF
But GE = AB [ ∵ ABEG is a parallelo¬gram and AB, GE forms a pair of opp. sides]
12 = AB ⇒ AF = 2AB
Hence Proved.

Question 4.
In the given figure ABCD is a paral¬lelogram. P, Q are the midpoints of sides AB and DC respectively. Show that 
Solution:

□ABCD is a parallelogram.
P, Q are the mid points of AB and CD.
Join Q, P.
Now AB = CD (Opp. sides of a //gm)
12AB = 12CD
PB = QC
Also PB // QC.
Now in □PBCQ;
PB = QC; PB//QC
Hence □PBCQ is a parallelogram.

Question 5.
ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD//BA as shown in the figure. Show that i) ∠DAC = ∠BCA
ii) ABCD is a parallelogram.

Solution:
Given that AABC is isosceles; AB = AC
AD is bisector of ∠QAC

i) In ΔABC, AB = AC ⇒ ∠B = ∠ACB
(angles opp. to equal sides)
Also ∠QAC = ∠B + ∠ACB
∠QAC = ∠BCA + ∠BCA
(∵∠BCA = ∠B)
⇒ 12∠QAC = 12 [2 ∠BCA]
⇒ ∠DAC = ∠BCA [ ∵ AD is bisector of ∠QAC]

ii) From (i) ∠DAC = ∠BCA
But these forms a pair of alt. int. angles for the pair of lines AD and BC; AC as a transversal.
∴ AD//BC
In □ABCD ; AB // DC; BC // AD
□ABCD is a parallelogram.

Question 6.
ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure). Show that 1) ΔAPB ≅ ΔCQD ii) AP = CQ.

Solution:
Given that □ABCD is a parallelogram.
BD is a diagonal.
AP ⊥ BD and CQ ⊥ BD
i) In ΔAPB and ΔCQD
AB = CD ( ∵ Opp. sides of //gm ABCD)
∠APB = ∠CQD (each 90°)
∠PBA = ∠QDC (alt. int. angles for the lines AB and DC)
∴ ΔAPB ≅ ΔCQD (AAS congruence)

ii) From (1) ΔAPB ≅ ΔCQD
⇒ AP = CQ (CPCT)

Question 7.
In Δs ABC and Δs DEF, AB = DC and AB//DE; BC = EF and BC//EF. Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that
i) ABED is a parallelogram
ii) BCFE is a parallelogram
iii) AC = DF
iv) ΔABC = ΔDEF

Solution:

Given that in ΔABC and ΔDEF
AB = DE and AB // DE
BC = EF and BC//EF.
i) In □ABED AB//ED and AB = ED
Hence □ABED is a parallelogram.

ii) In □BCFE; BC = EF and BC//EF
Hence □BCFE is a parallelogram.

iii) ACFD is a parallelogram (In a paral-lelogram opposite sides are equal).
So, AC = DF.

iv) Consider ΔABC = ΔDEF
AB = DE (given);
AC = DF (proved)
BC = EF (given)
∴ ΔABC ≅ ΔDEF (SSS congruency rule).

Question 8.
ABCD is a parallelogram. AC and BD are the diagonals intersect at ‘O’. P and Q are the points of trisection of the diagonal BD. Prove that CQ//AP and also AC bisects PQ.

Solution:
Given □ABCD is a parallelogram;
BD is a diagonal.
P, Q are the points of trisection of BD.
In ΔAPB and ΔCQD
AB = CD (•.• Opp. sides of //gm ABCD)
BP = DQ (given)
∠ABP = ∠CDQ (alt. int. angles for the lines AB//DC, BD as a transversal)
ΔAPB = ΔCQD (SAS congruence)
Similarly in ΔAQD and ΔCPB
AD = BC (opp. sides of //gm ABCD)
DQ = BP (given)
∠ADQ = ∠CBP (all int. angles for the lines AD//BC, BD as a transversal)
ΔAQD ≅ ΔCPB
Now in □APCQ
AP = CQ (CPCT of AAPB, ACQD)
AQ = CP (CPCT of AAQD and ACPB)
∴ □APCQ is a parallelogram.
∴ CQ//AP (opp. sides of//gm APCQ)
Also AC bisects PQ. [ ∵ diagonals of //gm APCQ]

Question 9.
ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH. Prove that EFGH is a square.
Solution:

Given that ABCD is a square.
E, F, G, H are the mid points of AB, BC, CD and DA.
Also AE = BF = CG = DH
In ΔABC; E, F are the mid points of sides AB and BC.
∴ EF//AC and EF = 12 AC
Similarly GH//AC and GH = AC
GF//BD and GF = 12 BD
HE//BD and HE = 12 BD

But AC = BD (∵ diagonals of a square)
∴ EF = FG = GH = HE
Hence EFGH is a rhombus.
Also AC ⊥ BD
(∵ diagonals of a rhombus)
∴ In //gm OIEJ [ ∵ 0I // EJ; IE // OJ]
We have ∠IOJ = ∠E
[ ∵ Opp. angles of a //gm]
∴ ∠E – 90°
Hence in quad. EFGH; all sides are equal and one angle is 90°.
∴ EFGH is a square.


AP Board Textbook Solutions PDF for Class 9th Telugu


Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 exam preparation. The AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 8 Quadrilaterals Ex 8.3 Books State Board syllabus with maximum efficiency.

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