BSEB Class 10 Maths Chapter 6 Triangles Ex 6.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.4 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

BSEB Class 10 Maths Chapter 6 Triangles Ex 6.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.4 Book Answers

BSEB Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks Solutions and answers for students are now available in pdf format. Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Book answers and solutions are one of the most important study materials for any student. The Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 books are published by the Bihar Board Publishers. These Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 textbooks are prepared by a group of expert faculty members. Students can download these BSEB STD 10th Maths Chapter 6 Triangles Ex 6.4 book solutions pdf online from this page.

Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks Solutions PDF

Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.4 Books Solutions with Answers are prepared and published by the Bihar Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of BSEB Class 10th Maths Chapter 6 Triangles Ex 6.4 Books Answers Solutions, then you are in the right place. Here is a complete hub of Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks. These Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Bihar Board.

Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Books Solutions

Board	BSEB
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	10th
Subject	Maths Chapter 6 Triangles Ex 6.4
Chapters	All
Provider	Hsslive

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BSEB Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks Solutions with Answer PDF Download

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BSEB Bihar Board Class 10th Maths Solutions Chapter 6 Triangles Ex 6.4

Question 1.
Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC.
Solution:

Question 2.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Solution:
In ∆s AOB and COD, we have :
∠AOB = ∠COD [Vert.opp.∠s]
and ∠OAB = ∠OCD [Alternate ∠s]
∴ By AA criterion of similarity, we have:

Hence, area (∆ AOB) : area (∆ COD) = 4 : 1

Question 3.
In the figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that

= 𝐴𝑂𝐷𝑂.

Solution:
Given : Two As ABC and DBC which stand on the same base BC but on the opposite sides of BC.
To prove :

= 𝐴𝑂𝐷𝑂.
Construction : Draw AE ⊥ BC and DF ⊥ BC.

Proof:
In ∆s AOE and DOF, we have :
∠AEO = ∠DFO = 90°
∠AOE = ∠DOF [Vertically opp. ∠s]
∴ By AA criterion of similarity, we have :

Question 4.
If the areas of two similar triangles are equal, prove that they are congruent.
Solution:
Given : Two ∆s ABC and DEF such that ∆ ABC – ∆ DEF
and Area (∆ ABC) = Area (∆ DEF)
To prove : ∆ ABC ≅ ∆ DEF

Proof:
∆ ABC ~ ∆ DEF
So, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
and 𝐴𝐵𝐷𝐸 = 𝐵𝐶𝐸𝐹 = 𝐴𝐶𝐷𝐹
To establish ∆ ABC ≅ ∆ DEF, it is sufficient to prove that

Hence ∆ ABC ≅ ∆ DEF [By SSS]

Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ALBC. Find the ratio of the areas of ∆ DEF and ∆ ABC.
Solution:
Since D and E are respectively, the mid-points of the sides AB and BC of ∆ ABC, therefore
DE [| AC, or DE || FC … (1)
Since D and F are respectively the mid-points of the sides AB and AC
∆ ABC, therefore

DF || BC, or DF || EC … (2)
From (1) and (2), we can say that DECF is a parallelogram.
Similarly, ADEF is a parallelogram.
Now, in ∆s DEF and ABC, we have :
∠DEF = ∠A [Opp. Zs of ||gm ADEF]
and ∠EDF = ∠C [Opp. Zs of ||gm DECF]
∴ By AA criterion of similarity, we have :
∆ DE ≅ ∆ AC

Hence, Area (∆ DEF) : Area (∆ ABC) =1:4.

Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
Given : ∆ ABC ~ ∆ PQR, AD and PM are the medians of ∆s ABC and PQR respectively.
To Prove : Area (ΔABC) Area (ΔPQR)=AD2PM2
Proof : Since ∆ ABC ~ ∆ PQR, therefore

Question 7.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of the diagonals.
Solution:
Given : A square ABCD. Equilateral ∆s BCE and ACF have been drawn on side BC and the diagonal AC respectively.
To prove : Area (∆ BCE) = 12(Area ∆ ACF)

Proof: ∆ BCE ~ ∆ ACF [All equilateral triangles are similar]

Question 8.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is ____________.
(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4
Solution:
Since ∆ ABC and ∆ BDE are equilateral triangles, they are equiangular and hence ∆ ABC – ∆ BDE

∴ (C) is the correct answer.

Question 9.
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
(A) 2 : 3
(B) 4 : 9
(C) 81 : 16
(D) 16 : 81
Solution:
Since the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides, therefore
ratio of areas = (4)² : (9)² = 16 : 81
∴ (D) is the correct answer.

BSEB Textbook Solutions PDF for Class 10th

Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks for Exam Preparations

Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 Textbook Solutions can be of great help in your Bihar Board Class 10th Maths Chapter 6 Triangles Ex 6.4 exam preparation. The BSEB STD 10th Maths Chapter 6 Triangles Ex 6.4 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 6 Triangles Ex 6.4 Books State Board syllabus with maximum efficiency.

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