AP Board Class 9 Maths Chapter 7 Triangles Ex 7.3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 7 Triangles Ex 7.3 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 9 Maths Chapter 7 Triangles Ex 7.3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 7 Triangles Ex 7.3 Book Answers

AP Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 9th Maths Chapter 7 Triangles Ex 7.3 books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 9th Maths Chapter 7 Triangles Ex 7.3 book solutions pdf online from this page.

Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Textbooks Solutions PDF

Andhra Pradesh State Board STD 9th Maths Chapter 7 Triangles Ex 7.3 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 7 Triangles Ex 7.3 Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 9th Maths Chapter 7 Triangles Ex 7.3 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 7 Triangles Ex 7.3 Textbooks. These Andhra Pradesh State Board Class 9th Maths Chapter 7 Triangles Ex 7.3 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 7 Triangles Ex 7.3 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	9th
Subject	Maths
Chapters	Maths Chapter 7 Triangles Ex 7.3
Provider	Hsslive

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AP Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Textbooks Solutions with Answer PDF Download

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AP State Syllabus 9th Class Maths Solutions 7th Lesson Triangles Exercise 7.3

Question 1.
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that, (i) AD bisects BC (ii) AD bisects ∠A.
Solution:

Given that in ΔABC, AB = AC
and AD ⊥ BC
i) Now in ΔABD and ΔACD
AB = AC (given)
∠ADB = ADC (given AD ⊥ BC)
AD = AD (common)
∴ ΔABD ≅ ΔACD (∵ RHS congruence)
⇒ BD = CD (CPCT)
⇒ AD, bisects BC.

ii) Also ∠BAD = ∠CAD
(CPCT of ΔABD ≅ ΔACD )
∴ AD bisects ∠A.

Question 2.
Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see figure). Show that:
(i) ΔABM ≅ ΔPQN
ii) ΔABC ≅ ΔPQR

Solution:
Given that
AB = PQ
AM = PN
i) Now in ΔABM and ΔPQN
AB = PQ (given)
AM = PN (given)
BM = QN (∵ BC = QR ⇒ 12BC = 12QR ⇒ BM = QN)
∴ ΔABM ≅ ΔPQN
(∵ SSS congruence)

ii) In ΔABC and ΔPQR
AB = PQ (given)
BC = QR (given)
∠ABC = ∠PQN [∵ CPCT of ΔABM and ΔPQN from (i)]
∴ ΔABC ≅ ΔPQR
(∵ SAS congruence)

Question 3.
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Solution:

In ΔABC altitude BE and CF are equal.
Now in ΔBCE and ΔCBF
∠BEC = ∠CFB (∵ given 90°)
BC = BC (common; hypotenuse)
CF = BE (given)
∴ ΔBEC ≅ ΔCBF
⇒ ∠EBC = ∠FCB (∵ CPCT)
But these are also the interior angles opposite to sides AC and AB of ΔABC.
⇒ AC = AB
Hence proved.

Question 4.
ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.
(Hint : Draw AP ⊥ BQ (Using RHS congruence rule)
Solution:

Given the ΔABC is an isosceles triangle and AB = AC
Let D be the mid point of BC; Join A, D.
Now in ΔABD and ΔACD
AB = AC (given)
BD = DC (construction)
AD = AD (common)
∴ ΔABD ≅ ΔACD (∵ SSS congruence)
⇒ ∠B = ∠C [∵ CPCT]

Question 5.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure). Show that ∠BCD is a right angle.

Solution:

Given that in ΔDBC; AB = AC; AD = AB
In ΔABC
∠ABC + ∠ACB = ∠DAC …………… (1)
[∵ exterior angle]
In ΔACD
∠ADC + ∠ACD = ∠BAC ………………(2)
Adding (1) & (2)
∠DAC + ∠BAC = 2 ∠ACB + 2∠ACD
[∵ ∠ABC = ∠ACB
∠ADC = ∠ACD]
180° = 2 [∠ACB + ∠ACD]
180° = 2[∠BCD]
∴ ∠BCD = 180∘2 = 90°
(or)
From the figure
∠2 = x + x = 2x
∠1 = y + y = 2y
∠1 + ∠2 = 2x + 2y
180° = 2 = (x + y)
∴ x + y = 180∘2 = 90°
Hence proved.

Question 6.
ABC is a right angled triangle in which ∠A = 90° and AB = AC, Show that ∠B = ∠C.
Solution:

Given ΔABC; AB – AC
Join the mid point D of BC to A.
Now in ΔADC and ΔADB
AD = AD (common)
AC = AB (giyen)
DC = DB (construction)
⇒ ΔADC ≅ ΔADB
⇒ ∠C = ∠B (CPCT)

Question 7.
Show that the angles of an equilateral triangle are 60° each.
Solution:

Given ΔABC is an equilateral triangle
AB = BC = CA
∠A = ∠B (∵ angles opposite to equal sides)
∠B = ∠C (∵ angles opposite to equal sides)
⇒ ∠A = ∠B = ∠C = x say
Also ∠A+∠B + ∠C =180°
⇒ x + x + x = 180°
3x = 180°
⇒ x = 1803 = 60°
Hence proved.

AP Board Textbook Solutions PDF for Class 9th Telugu

Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 7 Triangles Ex 7.3 exam preparation. The AP Board STD 9th Maths Chapter 7 Triangles Ex 7.3 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 7 Triangles Ex 7.3 Books State Board syllabus with maximum efficiency.

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