Triangles Exercise 6.6 Class 10 Maths: Triangles are some of the most ubiquitous geometric shapes found in everything from bridges and buildings to art and fashion. In mathematics, triangles are studied for their properties and characteristics, which can be employed to solve problems. Have you ever faced a situation where you have to solve triangle problems in your Class 10 Maths book and can not even understand how to start? Embibe brings you to complete NCERT solutions in this article. Here you will get detailed NCERT solutions for triangles Exercise 6.6 Class 10 Maths. 

Embibe’s NCERT Solutions for Exercise 6.6 Class 10 Maths covers all aspects of the topic and is presented in a simple manner so that it is easy to understand. Students can quickly get these NCERT Solutions for Class 10 Exercise 6.6 Maths by downloading the pdf file on the link given in this article. Learn how to find areas of similar triangles, criteria for similarity of triangles, and Pythagoras Theorem with step-by-step instructions.

NCERT Solutions for Triangles Exercise 6.6 Class 10 Maths: Overview

Exercise 6.6 Class 10 NCERT Solutions is an essential exercise for students studying in Class 10. It covers the basics of triangles, including the types of triangles, their properties and angles formed by three lines intersecting at a point. Solutions are detailed, along with simplified explanations on how to arrive at them. This makes it easy for students to understand the concepts and apply them to similar problems. 

Additionally, practice questions are present in these solutions for students to understand the underlying concepts better. Before we move on to Exercise 6.6 Class 10 NCERT Solutions, let us take a look at what students will learn from this chapter of the NCERT books.

Class	Class 10
Chapter Name	Triangles
Exercise Number	Exercise 6.6
Subject	Maths
Topic Name	Pythagoras Theorem
Language	English
Solution Type	In-text Solved Questions
Official Website	ncert.nic.in

NCERT Class 10 Maths NCERT Book Solutions: Download PDFs

Maths is an important subject that is extensively used in various fields. It is the foundation of all logical and numerical reasoning. After completing Class 10, students can choose to take up Maths as one of their subjects in Class 11 and 12. If they aim to pursue a career in mathematics or any other science stream, then mastering this subject will be very beneficial for them. 

NCERT Solutions for Class 10 Exercise 6.6 has been designed to help students prepare extensively for their exams. Our team of experts prepare the solutions with years of experience in teaching and preparing students for competitive exams. We have tried our best to ensure that the solutions cover all the questions in detail and provide a detailed explanation of the answers.

The table will give you access to the NCERT Solutions for Triangles Exercise 6.6 Class 10 Maths. We have provided links to the detailed solutions to all the questions in this exercise. These PDFs will be handy for students who want to revise their concepts before their exams.

Triangles Exercise 6.6 Class 10 Maths
Q.1. In the given figure, PS is the bisector of ∠QPR of ∆PQR. Prove that QSSR=PQPR.

Solution:

Given that, PS is angle bisector of ∠QPR.
Construct a line RT parallel to SP which meets QP produced at T. ∠QPS=∠SPR ……(1) ∠SPR=∠PRT
(As PS||TR, alternate interior angles) ….(2) ∠QPS=∠QTR (As PS||TR, corresponding angles)
…..(3) Using these equations, we may find ∠PRT=∠QTR from (2) and (3) So, PT=PR (Since ΔPTR is
isosceles triangle)
Now in ΔQPS and ΔQTR, ∠QSP=∠QRT (As PS||TR)
∠QPS=∠QTR (As PS || TR)
∠Q is common. ΔQPS~ΔQTR (by AAA property) So, QRQS=QTQP ⇒QRQS-1=QTQP-1 ⇒SRQS=PTQP
⇒QSSR=QPPT ⇒QSSR=PQPR

Q.2. Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see the given figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after12 seconds?

Solution:

Let AB be the height of tip of fishing rod from water surface and BC be the horizontal distance of fly from the tip of fishing rod.
Then, AC is the length of string. AC can be found by applying Pythagoras theorem in ΔABC. AC2=AB2+BC2
AC2=1.82+2.42 AC2=3.24+5.76 AC2=9.00 Thus, length of string out is 3 m.
Now, she pulls string at rate of 5 cm per second.
So, string pulled in 12 second=12×5=60 cm=0.6 m.

After 12 seconds, let us assume the fly to be at point D.
Length of string out after 12 second is AD. AD=AC- string pulled by Nazima in 12 second =3.00-0.6 =2.4 m In ΔADB,
AB2+BD2=AD2 ⇒1.82+BD2=2.42 ⇒BD2=5.76-3.24=2.52 ⇒BD=1.587 m Horizontal distance of fly =BD+1.2
=1.587+1.2 =2.787 =2.79 m

Q.3. In the figure, D is a point on hypotenuse AC of ∆ABC, such that BD⊥AC, DM⊥BC and DN⊥AB. Prove that : DM2=DN.MC

Solution:
Let us join DB.

DN||CB, DM||AB
Therefore, DNBM is a parallelogram.
Since, ∠B is 90°, therefore, DNBM is a rectangle. Hence, DN=MB, DM=NB and ∠CDB=∠ADB=90°
∠2+∠3=90o…(1) In ΔCDM ∠1+∠2+∠DMC=180° ∠1+∠2=90°…(2) In ΔDMB ∠3+∠DMB+∠4=180°
∠3+∠4=90°…(3)
From equation (1) and (2)
∠1=∠3
From equation (1) and (3) ∠2=∠4 So, ΔBDM~ΔDCM BMDM=DMMC ⇒DNDM=DMMC ⇒DM2=DN.MC Hence, proved.

Exercise	PDF
NCERT Solutions for Triangles Exercise 6.6 Class 10 Maths	Get Solutions

NCERT Solutions for Chapter 6 Class 10 Maths: Chapter Description

Students can quickly grasp the problems presented in this chapter with thorough explanations using Embibe’s NCERT answers, which will help them practise the chapter and master the topic. The solutions PDFs provided in this article are elaborate and complete, and any learner should be able to follow them.

Coming to the concepts covered in the Chapter 6 Exercise 6.6 Class 10 NCERT Solutions, students will learn how similar triangles follow similarities in sizes and angles and how to determine similarities to solve problems. Through exercises, they will also learn how to determine such similarities and further understand how even to find areas of similar triangles.

CBSE Class 10 NCERT Maths book Chapter 6 deals with these concepts of triangles in the table below:

Ex 6.1	Introduction
Ex 6.2	Similar Figures
Ex 6.3	Similarity of Triangles
Ex 6.4	Criteria of Similarity of Triangles
Ex 6.5	Areas of Similar of Triangles
Ex 6.6	Pythagoras Theorem
Ex 6.7	Summary

Benefits of Studying from NCERT Solutions for Ex 6.6 Class 10 Maths

The NCERT Solutions for Ex 6.6 Class 10 Maths from Embibe is a collection of detailed answers to all questions and problems given in the NCERT textbook. It also includes important notes, tips, and suggestions that will help you understand the concept better.

Here are some reasons why you should choose Embibe’s NCERT solutions for Triangles Exercise 6.6 Class 10 Maths:

1. The NCERT Solutions for Ex 6.6 Class 10 Maths have been developed keeping in mind the latest board exams, which makes them very relevant to current topics for CBSE. This makes it easier for students to study from these solutions during their exam preparation and get better grades in their exams.

2. It helps students better organise their study material and know what topics to focus on more than others. It also helps them know what areas they need to revise and how much time they should spend on each topic.

3. By solving the NCERT solutions, you can quickly strengthen your basics, understand them better, and easily remember question-solving methods.

4. Students can overcome their doubts and get an overall view of the topic by studying from Embibe’s NCERT Solutions for Ex 6.6 Class 10 Maths.

5. It facilitates self-learning through practice and revision, which will help improve performance in exams, quizzes, tests and other assessments related to the topics.

FAQs on Triangles Exercise 6.6 Class 10 NCERT Solutions

Here we are providing some of the most frequently asked questions (FAQs) on Ex 6.6 Class 10 Maths NCERT Solutions:

Q.1: Which is the best website for NCERT Maths Solution Class 10?

Ans: Embibe’s NCERT solutions for Class 10 Maths are written by experts and are simple and complete. We have solutions for all the questions in NCERT books.

Q.2: Is NCERT Maths textbook enough for Class 10 Board Exams?

Ans: For the Class 10 board exam, you will find the NCERT maths textbook reasonably sufficient. However, practise previous year’s papers and sample papers to understand better what you will expect at the exam.

Q.3: How many exercises are in class 10 triangles?

Ans: There are around 6 exercises on concepts of triangles in NCERT Class 10.

Q.4: How can I score the best in Class 10 Maths Chapter 6 Exercise 6.6 Triangles?

Ans: All you need to do is follow a strategy that you can use for any question, whether they are based on simple formulas or concepts related to the Class 10 Triangles chapter. Therefore, it is good to use NCERT Solutions from Embibe, which are detailed and simplified.

Q.5: What’s the underlying concept of the Chapter 6 Triangles?

Ans: In Chapter 6, Triangles, students study Similar Figures, Similarity of Triangles, Criteria for Similarity of Triangles, Area of Similar Triangles, and Pythagoras Theorem.

Also Check,

NCERT Solutions for Class 6 Maths	NCERT Solutions for Class 6 Science
NCERT Solutions for Class 7 Maths	NCERT Solutions for Class 7 Science
NCERT Solutions for Class 9 Maths	NCERT Solutions for Class 9 Science
NCERT Solutions for Class 10 Maths	NCERT Solutions for Class 10 Science
NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics

We hope this article on the NCERT Solutions for Mathematical Reasoning Exercise 6.6 Class 10 Maths proves helpful. However, if you have any questions about the Ex 6.6 Class 10 Maths NCERT solutions or any other queries, do not hesitate to drop a comment below. We will get back at the earliest.

Stay tuned to Embibe for the latest updates and information on Class 10 Exercise 6.6 NCERT solutions and the latest academic articles.