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Chapter 6 Triangles - NCERT Solutions for Class 10 Mathematics CBSE - TopperLearning

Chapter 1 - Real Numbers. Chapter 2 ,aths Polynomials. Chapter 4 - Quadratic Equations. Chapter 5 - Arithmetic Progressions. Chapter 6 - Triangles. Chapter 7 - Coordinate Geometry. Chapter 8 - Introduction to Trigonometry. Chapter 9 - Some Applications of Trigonometry. Chapter 10 - Circles. Chapter 11 - Constructions. Chapter 12 - Areas Related to Circles.

Chapter 13 cpass Surface Areas and Volumes. Chapter 14 - Statistics. Chapter ncert solutions of chapter 6 class 10th maths - Probability. Students were already introduced to the concept of Triangles in Class 9 wherein they studied properties such as congruence of Triangles. The introduction part of the chapter basically acts as a window for the students so that they are able to get solutiions insight as to what would they be learning new under the topic of Triangles.

In this section of the Clxss 10 Maths Chapter 6, students are introduced to the concept of similar figures. Students are taught the basis of similarity in figures such as squares or equilateral triangles with the same lengths of the sides, circles with the same radii. As the students progress through this topic, they get to understand that similar figures can have the same shape but not necessarily the exact size.

The questions from this topic mostly ask students to prove similarity between figures by applying the theorems. Once the students are made familiar with the concept of similarity, they are then introduced to the criteria under which two or more triangles are deemed ncert solutions of chapter 6 class 10th maths. A thorough understanding of this topic will allow students to form the base for solving complex problems in higher mathematics.

This section outlines and explains the criteria for ncert solutions of chapter 6 class 10th maths similarity of triangles. The basic criteria for two triangles to be called similar include: if their corresponding angles are equal and if the corresponding sides of the triangles are in the same ratio or proportion.

Students will be able to visualise the theorems as they are illustrated with the help of proper examples. Students can understand the formula and learn the process for finding the surface area of similar triangles clasx this section.

Students have already learnt the theorem and its proof in Class 9. In this section, students will learn how to prove this theorem by employing the concept of similarity of triangles. The summary comprises all the topics that you have studied in the chapter. Going through the summary will allow you to recollect all that you have learnt in the chapter including the important concepts, theorems.

The list of exercise in the Maths Class 10 Chapter 6 has been provided below:. Students using these solutions to prepare for the exam benefit due to the following reasons:.

The solutions have been provided by experts making them reliable and free of errors. Students can learn and understand by using these solutions at their convenience with the help of physical copy. Students are able to get a good command over the subject which helps them to improve their scores as. Using these solutions can yield many benefits for the students as they can refer to them if they are stuck with a problem or are having ncedt gaining command over any topic.

Moreover, all the solutions have been provided in a systematic manner so that students are able to make judicious use of ncert solutions of chapter 6 class 10th maths time as they prepare for the exams.

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Some bridges have triangular constructions, and the Egyptians made triangular-shaped pyramids. The shapes help surveyors use triangulation to define the distance of a specific point from two other points of a known distance aloof.

Triangulation is used to measure distances around corners and when drilling pits, and carpenters use a right-angled triangle to get measurements. Right-angled triangles are used beside trigonometry to solve real-world distance problems, such as the length a ladder of a known length can go up towards a wall if the angle the ladder makes with the ground is also known. This concept also helps determine the flight path the distance traveled from the beginning point and bearing of a plane that travels at a known speed for some hours, turns at a known angle at the same velocity, and continues to fly for a known number of hours.

A sandwich may be formed like a triangle. A staircase makes a right-angled triangle, with its length being the hypotenuse. Also, a right-angled triangle forms when one stands at the top of the tower, observes an oncoming ship and ventures to calculate the distance between the boat and the bottom of the pillar or the angle of elevation from the top.

All the solutions have been prepared in an elaborate and step-by-step manner. You can use these solutions not only for exam preparation but also to complete your assignments and homework. Our academic experts have optimized the NCERT solutions not only for the board exams but also for competitive exams and olympiads. Calculate the length of the side of the rhombus if the lengths of the diagonals of a rhombus are given as 16 cm and 12 cm.

Calculate the distance from the top of the pole to the far end of the shadow if the height of the flag pole is 18 m the length of its shadow is 9. An equilateral triangle is given with the length of the sides as 8 cm.

Find each of its altitudes. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. A ladder 10 m long reaches a window 8 m above the ground. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.

How far from the base of the pole should the stake be driven so that the wire will be taut? An aeroplane leaves an airport and flies due north at a speed of km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of km per hour. Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. Prove that Solution:. Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides. In the given figure, two chords Ab and CD of a circle intersect each other at the point P when produced outside the circle.

Nazima is fly fishing in a stream. The trip of her fishing rod is 1. Assuming that her string from the trip of the rod to the fly is that, how much string does she have out see the figure? If she pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds? Two figures having the same shape but not necessarily the same size are called similar figures Two figures having the same shape as well as same size are called congruent figures Note that all congruent figures are similar but the similar figures need not be congruent.

Two polygons of the same number of sides are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion. Two triangles are similar if i their corresponding angles are equal and ii their corresponding sides are in the same ratio or proportion Note : If the corresponding angles of two triangles are equal, then they are known as equiangular triangles.

The ratio of any two corresponding sides in two equiangular triangles is always the same. Basic Proportionality Theorem If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then other two sides are divided in the same ratio.

Converse of BPT If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side,. Formulae Handbook for Class 10 Maths and Science.

Solution: Ex 6. Solution: Triangles Class 10 Ex 6. Recall that your have proved it in class IX Solution: Ex 6. Recall that your have done it in class IX Solution: Ex 6. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form : Solution: Ex 6. Prove that: Solution: Ex 6. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : 81 Triangles Class 10 Ex 6.

CD Solution: Ex 6.

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