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NCERT Solutions for Exercise 6.4 Class 10 Maths Chapter 6 Triangles are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 maths ex 6.4 states the theorem “The square of the ratio of the corresponding sides of two comparable triangles is equal to the ratio of their areas”. Also discusses about criteria to find similarities between triangles and learn about simple geometry problems.
NCERT solutions for exercise 6.4 Class 10 Maths chapter 6 Triangles discusses mainly on the ratio of area and ratio of squared sides. 10th class Maths exercise 6.4 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
Triangles Class 10 Chapter 6 Exercise: 6.4
Q1 Let and their areas be, respectively, 64
and 121
. If EF = 15.4 cm, find BC.
Answer:
( Given )
ar(ABC) = 64 and ar(DEF)=121
.
EF = 15.4 cm (Given )
Answer:
Given: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O.
AB = 2 CD ( Given )
In
(vertically opposite angles )
(Alternate angles)
(Alternate angles)
(AAA similarity)
Q3 In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that
Answer:
Let DM and AP be perpendicular on BC.
In
(Each
)
(Vertically opposite angles)
(AA similarity)
Since
Q4 If the areas of two similar triangles are equal, prove that they are congruent.
Answer:
Let , therefore,
(Given )
(SSS )
Answer:
D, E, and F are respectively the mid-points of sides AB, BC and CA of . ( Given )
and DE||AC
In ,
(corresponding angles )
(corresponding angles )
(By AA)
Let be x.
Similarly,
and
Answer:
Let AD and PS be medians of both similar triangles.
Purring these value in 1,
In
(proved above)
(proved above)
(SAS )
Therefore,
From 1 and 4, we get
Answer:
Let ABCD be a square of side units.
Therefore, diagonal =
Triangles form on the side and diagonal are ABE and
DEF, respectively.
Length of each side of triangle ABE = a units
Length of each side of triangle DEF = units
Both the triangles are equilateral triangles with each angle of .
( By AAA)
Using area theorem,
(A) 2: 1 (B) 1: 2 (C) 4 : 1 (D) 1: 4
Answer:
Given: ABC and BDE are two equilateral triangles such that D is the mid-point of BC.
All angles of the triangle are .
ABC
BDE (By AAA)
Let AB=BC=CA = x
then EB=BD=ED=
Option C is correct.
Q9 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
Answer:
Sides of two similar triangles are in the ratio 4: 9.
Let triangles be ABC and DEF.
We know that
Option D is correct.
Class 10 Maths chapter 6 exercise 6.4: Most of the questions are based on the ratio of areas of similar triangles in exercise 6.4 Class 10 Maths, but we should be also aware of some basic geometry which helps to solve problems of NCERT solutions for Class 10 Maths exercise 6.4. We should know the properties of the trapezium and the criterion of similarity of triangles. Questions given in the Exercise 6.4 Class 10 Maths are very important for the board exam. Students can also access Triangles Class 10 Notes here and use them for quickly revision of the concepts related to Triangles.
Also, See
No, it is not always true but it is proved in NCERT solutions for Class 10 Maths 1 exercise 6.4 that ratio of areas of two similar triangles is equal to the square of ratio of corresponding sides of that triangles.
No, it is not always true but it is proved in NCERT solutions for Class 10 Maths 1 exercise 6.4 that ratio of areas of two similar triangles is equal to the square of ratio of corresponding sides of that triangles.
RHS rule is used to prove similarity
Yes, by using theorem 6.6 given in NCERT solutions for Class 10 Maths 1 exercise 6.4, we can prove this.
Ratio of areas of similar triangles is equal to the ratio of square of corresponding sides of that triangles.
Sides of similar triangles are in ratio 25:36, find the ratio of areas of triangle.
Ratio is 625:1296.
Yes, they are similar by AAA rule.
Two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Exam Date:01 January,2025 - 14 February,2025
Exam Date:01 January,2025 - 14 February,2025
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
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Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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