NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Students can download the optional exercise of Class 10 Maths Chapter 6 in PDF format for session 2024-25. It is useful for High School UP Board and CBSE Board students. You can get the 10th Maths Chapter 6 Solutions in Hindi and English medium.
As we know that Utter Pradesh Board using NCERT Books for their Board exams. So download UP Board Solutions for Class 10 Maths Chapter 6 here free of cost. You can share your doubts and ask questions from your classmates through Discussion Forum. Visit to Discussion Forum to share your knowledge. This platform is here to discuss the doubts of all students with experts and teachers. For any trouble, please contact us for help. We will try to solve your difficulty at our level best.

NCERT Solutions for Class 10 Maths chapter 6 are given for Revision for Exams. Complete Exercises solutions and a brief description about triangles, similarity of triangles, theorems and the facts related to this chapter are given below. It will help the students to enhance their knowledge about the chapter triangles and the mathematician involved. Download the NCERT Textbooks of all subjects of class 10 updated for 2024-25.

OBJECTIVES OF THE CHAPTER – SIMILAR TRIANGLES

To identify similar figures, distinguish between congruent and similar triangles, prove that if a line is drawn parallel to one side of a triangle then the other two sides are divided in the same ratio, state and use the criteria (Criteria means a standard which is established so that judgement or decision, especially a scientific one can be made) for similarity of triangles viz. AAA, SSS and SAS.
To verify and use results given in the curriculum based on similarity theorems. To prove the Baudhayan/Pythagoras Theorem and apply these results in verifying experimentally (or proving logically) problems based on similar triangles.

History of similar triangles

A Greek mathematician Thales gave an important relation relating to two equiangular triangles that ‘The ratio of any two corresponding sides in two similar triangles is always the same. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio’. Which is known as the Basic Proportionality Theorem or the Thales Theorem.
There are so many other important theorems based on similar triangles like If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar. Or if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Download CBSE board Exams papers, for the questions based on BPT in board exams.

Historical Facts!

1. We know that Pythagoras theorem is popular. It has wide range of applications. In ancient Indian Maths society done well. Bodhayan (800 BC) wrote ‘Sulb Sutras’. It depicts Pythagoras theorem. Bhashkaracharya and Brahmaputra gave different proofs of it.
2. We all know that Leonardo De Vinchi was the great artist. He was an architect. He was famous for his painting ‘Mona Lisa’. He gave a beautiful proof for this theorem.
3. Thales of Miletus (624 – 546 BC, Greece) was the first known philosopher with math knowledge. He worked as 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. He used the shadows and principle of similar triangles. We could get the Height of pyramids using facts of trigo.
4. Brahma Gupta’s theorem (628 A.D.):
The rectangle contained by any two sides of a triangle, is equal to rectangle contained by altitude drawn to the third side and the circum diameter.
5. Galileo Galilei explained about the universe. He told no one can read it until we have learnt its language. Its language includes the letters like triangles, circles and other Maths figures. Without learning, it is impossible to comprehend a single word.