Class 10 Maths NCERT solutions of Chapter 6- Triangles(PDF)
Class 10 Maths NCERT solutions of Chapter 6- Triangles is the fundamental chapter of the geometry, chapter 6 – Triangles of class 10 maths NCERT is based on the properties of triangles like basic proportionality theorem, the similarity of triangles and Pythagoras theorem. All questions of Class 10 Maths NCERT solutions of Chapter 6- Triangles are solved by an expert teacher as per the CBSE norms.
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NCERT Solutions Class 10 Maths Chapter 6, Triangle, is a part of the Geometry which constitutes 15 marks of the total marks of 80. Based on the CBSE Class 10 examination prospectus, this chapter-6 has the second-most elevated weightage. Consequently, having a clear understanding of the ideas, theorems, and problem-solving techniques, in this section is compulsory to score well in the Board assessment of class 10 maths.
Main topics covered in this chapter include:
From your previous classes, you know about triangles and a considerable lot of their properties. In Class 9, you have studied the congruency of the triangles in detail. In this part, we will consider those triangles which have a similar shape however not really a similar size. Two triangles having a similar shape (and not really a similar size) are called similar triangles. In chapter 6 of class 10 maths, we will study the similarity of triangles and application of this property in giving a basic verification of Pythagoras Theorem learned before.
In Class 9, you have seen that all circles with similar radii are congruent, all squares with a similar side length are congruent and all equilateral triangles with a similar side length are congruent. The chapter clarifies the similarity of triangles by playing out the applicable action. Similar triangles are two triangles having a similar shape yet not really a similar size.
Similarity of Triangles
The topic recalls triangles and its similarities. Two triangles are similar if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion). It explains Basic Proportionality Theorem and different theorems are discussed performing various activities.
Basic Proportionality Theorem- If a line is drawn parallel to one of the sides of a triangle such that it intersects two sides then it divides the other two sides of the triangle in the same ratio.
Criteria for Similarity of Triangles
In the previous section, we stated that two triangles are similar (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion). The topic discusses the criteria for similarity of triangles referring to the topics we have studied in earlier classes. It also contains different theorems explained with proper examples.
AA rule – If in two triangles two corresponding angles are the same of then both of triangles are similar to each other.
SAS rule – If in two triangles two correspondings sides are in proportion and the angles subtended by them are also equal then triangles are similar to each other.
∠B = ∠E
ΔABC ∼ ΔDEF (SAS rule)
SSS rule- If all corresponding sides of two triangles in proportion then both of the triangles are similar to each other.
ΔABC ∼ ΔDEF (SSS rule)
Areas of Similar Triangles
You have learned that in two similar triangles, the ratio of their corresponding sides is the same. The topic Areas of Similar Triangles consists of theorem and relatable examples to prove the theorem.
The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
You are already familiar with the Pythagoras Theorem from your earlier classes. You have also seen proof of this theorem in Class 9. Now, we shall prove this theorem using the concept of similarity of triangles. Hence, the theorem is verified through some activities and make use of it while solving certain problems
Download the PDF of class 10 NCERT solutions PDF of chapter 6- Triangles