NCERT Solutions for Maths Chapter 6 Triangles Class 10
NCERT Solutions for Class 10 Maths Chapter 6, called Triangles are super important study materials for CBSE Class 10 students. This chapter aligns perfectly with the CBSE Syllabus for 2023-24, covering lots of rules and theorems. Sometimes, students get puzzled about which theorem to use. Here students will get NCERT solutions for Class 10 chapter wise. Practice these solutions for triangles class 10 to command the concepts.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles NCERT solutions created at Careers360 are made to be crystal clear, explaining every step. Subject experts have created these solutions to help you prepare well for your board exams. They're not just for exams but also for tackling homework and assignments.
CBSE Class 10 exams often have questions from NCERT textbooks. So, Chapter 6's NCERT Solutions for Class 10 Maths are your best bet for getting ready and being able to tackle any kind of question from this chapter. We strongly recommend practicing these solutions regularly to ace your Class 10 board exams. Theorems of triangles class 10 pdf download are available freely, students can download using below link.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles PDF Free Download
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NCERT Solutions Class 10 Maths Chapter 6 - Important Points
Similar Triangles - A pair of triangles that have equal corresponding angles and proportional corresponding sides.
Equiangular Triangles:
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Criteria for Triangle Similarity:
Angle-Angle-Angle (AAA) Similarity
Side-Angle-Side (SAS) Similarity
Side-Side-Side (SSS) Similarity
Basic Proportionality Theorem:
Converse of Basic Proportionality Theorem:
Free download NCERT Solutions for Class 10 Maths Chapter 6 Triangles PDF for CBSE Exam.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles (Intext Questions and Exercise)
Q2 In Fig. 6.35, , and . Find
Answer:
Given : , and
(DOB is a straight line)
In
Since , , so
( Corresponding angles are equal in similar triangles).
Q14 Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that
Answer:
(given)
Produce AD and PM to E and L such that AD=DE and PM=DE. Now,
join B to E,C to E,Q to L and R to L.
AD and PM are medians of a triangle, therefore
QM=MR and BD=DC
AD = DE (By construction)
PM=ML (By construction)
So, diagonals of ABEC bisecting each other at D,so ABEC is a parallelogram.
Similarly, PQLR is also a parallelogram.
Therefore, AC=BE ,AB=EC and PR=QL,PQ=LR
(Given )
(SSS similarity)
...................1 (Corresponding angles of similar triangles)
Similarity,
........................2
Adding equation 1 and 2,
............................3
In
( Given )
( From above equation 3)
( SAS similarity)
Q16 If AD and PM are medians of triangles ABC and PQR, respectively where , prove that
Answer:
( Given )
............... ....1( corresponding sides of similar triangles )
....................................2
AD and PM are medians of triangle.So,
..........................................3
From equation 1 and 3, we have
...................................................................4
In
(From equation 2)
(From equation 4)
(SAS similarity)
Q7 Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Answer:
In AOB, by Pythagoras theorem,
In BOC, by Pythagoras theorem,
In COD, by Pythagoras theorem,
In AOD, by Pythagoras theorem,
Adding equation 1,2,3,4,we get
(AO=CO and BO=DO)
Hence proved .
Q8 (1) In Fig. 6.54, O is a point in the interior of a triangle ABC, OD BC, OE AC and OF AB. Show that
Answer:
Join AO, BO, CO
In AOF, by Pythagoras theorem,
In BOD, by Pythagoras theorem,
In COE, by Pythagoras theorem,
Adding equation 1,2,3,we get
Hence proved
Q8 (2) In Fig. 6.54, O is a point in the interior of a triangle ABC, OD BC, OE AC and OF AB.
Answer:
Join AO, BO, CO
In AOF, by Pythagoras theorem,
In BOD, by Pythagoras theorem,
In COE, by Pythagoras theorem,
Adding equation 1,2,3,we get
Q13 D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that
Answer:
In ACE, by Pythagoras theorem,
In BCD, by Pythagoras theorem,
From 1 and 2, we get
In CDE, by Pythagoras theorem,
In ABC, by Pythagoras theorem,
From 3,4,5 we get
NCERT solutions for class 10 maths chapter 6 Triangles Excercise: 6.6
Q1 In Fig. 6.56, PS is the bisector of . Prove that
Answer:
A line RT is drawn parallel to SP which intersect QP produced at T.
Given: PS is the bisector of .
By construction,
(as PS||TR)
(as PS||TR)
From the above equations, we get
By construction, PS||TR
In QTR, by Thales theorem,
Hence proved.
Q2 In Fig. 6.57, D is a point on hypotenuse AC of triangle ABC, such that BD AC, DM BC and DN AB. Prove that :
Answer:
Join BD
Given : D is a point on hypotenuse AC of D ABC, such that BD AC, DM BC and DN AB.Also DN || BC, DM||NB
In CDM,
In DMB,
From equation 1 and 2, we get
From equation 1 and 3, we get
In
(By AA)
(BM=DN)
Hence proved
NCERT Class 10 Maths solutions chapter 6 - Topics
Similarity of triangles
Theorems based on similar triangles
Areas of similar triangles
Theorems related to Trapezium
Pythagoras theorem
Also get the solutions of individual exercises-
Key Features Of NCERT Solutions for Class 10 Maths Chapter 6
Comprehensive Coverage: NCERT Solutions for class 10 triangles cover all the topics and concepts included in the CBSE syllabus for this chapter.
Detailed Explanations: The class 10 triangles solutions provide step-by-step and clear explanations for each problem, making it easy for students to understand the concepts and solutions.
CBSE-Aligned: These triangle solutions class 10 are closely aligned with the CBSE curriculum for Class 10, ensuring that students are well-prepared for their board exams.
Illustrative Examples: The triangle solutions class 10 often include illustrative examples to help students grasp the application of mathematical concepts.
Clarity: Concepts are explained in a simple and straightforward manner, ensuring that students can follow along and build a strong foundation in mathematics.
NCERT Solutions Of Class 10 - Subject Wise
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How to use NCERT Solutions for Class 10 Maths Chapter 6 Triangles?
First of all, go through all the concepts, theorems and examples given in the chapter.
This chapter needs so much use of theorems. So you have to memorize these conditions and theorems to solve the problems.
After this, you can directly jump to practice exercises.
While solving the practising the exercises, if you face any problem in a question then you take the help of NCERT solutions for class 10 maths chapter 6.
Once you have done the practise exercises you can move to previous year questions.
Keep working hard & happy learning!