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NCERT Solutions for Class 10 Maths Chapter 6 Triangles (Ex ) Exercise

These solutions are useful for Board exams You can share your doubts and ask questions from your classmates through Tiwari Academy Discussion Forum. Complete Exercises solutions and a brief description about triangles, similarity of triangles, theorems and the facts related to this chapter are given. It will help the students to enhance their knowledge about the chapter triangles and the mathematician involved.

Similarity of geometric figures is an important concept of Euclidean geometry. Similarity in a geometric transformation of one figure into the other figure such that the measure of all linear elements of one figure are in proportion to the corresponding linear elements of the other figure.

Two triangles or any 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. Ncert solutions class 10 maths ch 6 ex 6.2 note congruent figures are similar but the similar figures need not be congruent. Area Theorem: The ratio of the areas of two similar triangles is equal to the square of ncert solutions class 10 maths ch 6 ex 6.2 note ratio of their corresponding sides.

Pythagoras theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Visit to Discussion Forum to share your knowledge. This platform is being maintained ncert solutions class 10 maths ch 6 ex 6.2 note discuss the doubts of all students with experts and teachers.

For any inconvenience, please contact us for help. We will try to solve your difficulty as soon as possible. What is meant by Similarity or Similar Triangle?

What is Area Theorem in Class 10? State Pythagoras theorem? State Converse of Pythagoras theorem. To verify and use results given in the curriculum based on similarity theorems. There are so many other important theorems based on similar triangles like If in two triangles, sides of one triangle are proportional to i.

Or if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Historical Facts! Pythagoras theorem is famous because of its wide range of applications.

Thales of Miletus � BC, Greece was the first known philosopher and mathematician. He is credited with the first use of deductive reasoning in geometry.

He discovered many propositions in geometry. He is believed to have found the heights of the pyramids in Egypt, using shadows and principle of similar triangles.

Height of pyramids can also be find using applications of trigonometry. According to Galileo Galilei, the universe cannot be read until we have learnt the language in which it is written. It is written in mathematical language and the letters are triangles, circles and other Ncert Solutions Class 10th Maths Chapter 5 Login geometrical figures, without which it is humanly impossible to comprehend a single word. Determine this is a right triangles.

In case of a right triangle, write the length of its hypotenuse. Sides of triangle: 7 cm, 24 cm and 25 cm. Squaring these sides, we get 49, and We know that the hypotenuses is the longest side in right angled triangle. Hence, its length is 25 cm. ABC is an isosceles triangle right angled at C. Hence, the triangle ABC is a right angled triangle. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

Let OA is wall and AB is ladder. Chapter 7: Coordinate Geometry �.

Abstract:

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Using converse of B. Recall that your have done it in class IX Solution:. State which pairs of triangles in the given figures are similar.

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :. Prove that: Solution:. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. If the areas of two similar triangles are equal, prove that they are congruent. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

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 its diagonals. Areas of these triangles are in the ratio a 2 : 3 b 4 : 9 c 81 : 16 d 16 : Sides of triangles are given below.

Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. CD Solution:. ABC is an isosceles triangle right angled at C. ABC is an equilateral triangle of side la. 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. It has a total of 10 questions with each one covering different fundamentals.

To understand it better, let us walk you through the concepts covered in every question. The first question contains two triangles, each of them having the same condition as DE BC. We need to find out the values of EC and AD in these respective figures. The students can find out the values easily by using the basic proportionality theorem and properties of similar triangles. For any further issues, you can check the solution of ex 6.

The second question consists of a triangle having sides PQ and QR, respectively. The measurements of the sides are provided. Following this, the students need to find out whether EF QR.

The question can again be solved using properties of similar triangles. If the ratios of sides are similar, then, they are parallel to each other. Else, they are not. They can easily do this by the basic proportionality theorem. This question is quite similar to the previous one.

The students can solve this in Ncert Solutions Of Class 10th Maths Chapter 4 Exercise 4.3 Note three steps by the properties of similarity of triangles. Both these questions in the exercise are based on the same concept of basic proportionality theorem and similarity of triangles.

Some parallel conditions are given, and students need to prove that one of the lines in the triangle is parallel to the base of the triangle. Use the concepts wisely to prove the given questions. While solving this question, the students need to recall the concept of mid-point theorem they learnt in Class 9.

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