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Xam Idea Class 10 Maths Chapter 7 Solutions: Triangles

Xam Idea Class 10 Maths Solutions for Chapter 7 ‘Triangles’ are one of the most crucial study resources for CBSE exams. The questions cover all the concepts of the chapter such as the basics of triangles, area and perimeter of a triangle, similarity criteria of triangles and the Pythagoras theorem. All the questions are presented in a concise and exquisite form for your quick and better understanding before the exams. These solutions to all Xam Idea Solutions exercises will help you recapitulate all the topics of the chapter easily and quickly.

Overall, the chapter contains 6 exercises and 71 questions that are based on the discussed set of topics of the chapter. The exercises cover a mix of questions such as short answer type questions, long answer type questions, true/ false, HOTS (higher-order thinking skills), value-based questions etc. All the questions are formed in accordance with the latest guidelines prescribed by CBSE and NCERT. The detailed explanation of all the important topics helps to score excellent marks in the board exams. They will also help you participate and perform well in the national level Maths olympiads.

The team of Instasolv provides you with formulated and altered solutions for Xam Idea Class 10 Maths book that is written or designed in a simple and easy to understand language. By opting our solutions, you will be able to eliminate all your doubts and confusions regarding this chapter quite easily. We provide you with accurate and qualitative solutions for your revision of all the concepts of Class 10 Maths. This will surely help you in your last minute revision before the exams.

Important Topics Of The Xam Idea Class 10 Maths Solutions Chapter 7: Triangles

In this chapter, you are going to study different theorems and similarities of triangles. The chapter covers topics such as the similarity criteria of two quadrilaterals having the same number of sides or same angles, similarity criteria of the triangles which are done by different theorems like SAS, AA, AAA etc. You will also learn the proof of Pythagoras theorem in this chapter. It also includes all the proof of the different theorems of triangles and vice versa. It covers all the properties of triangles and the difference between congruence and similarity.

Introduction

  • A triangle can be defined as a polygon which has three angles and three sides. The sum of all interior angles of a triangle is 180 degrees and the sum of all exterior angles of a triangle is 360 degrees.
  • On the basis of the angles and length of different sides, the triangles are classified into the following types
  1. Scalene triangle- All three sides are of different measures i.e no side is equal to others.
  2. Equilateral triangle- All the sides are equal and are of the same measurement.
  3. Isosceles triangle- Two sides are of equal length and have equal angles.
  4. Right-angled triangle- One angle is 90 degrees and the side opposite to 90 degrees is the hypotenuse.
  5. Acute angled triangle – All the angles are less than 90 degrees.
  6. Obtuse angled triangle- It has one angle of more than 90 degrees.
  • Any two figures (quadrilaterals or triangles) which have the same number of sides are similar only when their corresponding sides or angles are equal to the sides or angles of the other figure or when the ratio of corresponding sides of the two triangles or quadrilaterals are equal.

Similarity Criteria Of Triangles

  • Side-Side-Side (SSS) similarity criteria- In this theorem, you will learn that if the corresponding sides of any two triangles are in the same ratio then the triangles are similar.
  • Angle-Angle-Angle (AAA) similarity criteria- The theorem is the same as SSS similarity but in this all the corresponding angles of any two triangles are equal then the triangles are similar.
  • Angle-Angle (AA) similarity criteria– If two angles of any triangle are equal to the two angles of other triangles then the third angle will also be similar as the sum of angles of a triangle is 180 degrees and the triangles will be similar.
  • Side-Angle-Side (SAS) similarity criteria– This theorem includes the sides as well as the angle of the triangle when two corresponding sides of the triangles are in equal ratio and the angle between two sides is also equal then the triangles will be considered as similar. 
  • The ratio of corresponding sides of two triangles is always equal to the Ratio of corresponding perimeters of that particular triangle.
  • The ratio of corresponding sides of any two similar triangles will be equal to the Ratio of corresponding altitudes or medians of the same triangles.
  • The ratio of corresponding sides of similar triangles is also equal to the  Ratio of corresponding angle bisector segments of those triangles.

Areas of Similar Triangles and Pythagoras Theorem

  • By this theorem, you will learn that if two triangles are similar then the square of the ratio of their corresponding sides will be equal to their area. 
  • By the Pythagoras theorem, you will get to know about the right angle triangle. The theorem states that in a right angle triangle the square of the hypotenuse (the longest side) is equal to the sum of squares of the other two sides.

Exercise Discussion Of Xam Idea Class 10 Maths Solutions Chapter 7 Triangles

Very Short Answer Type Questions

This section contains 6 questions which need to be answered in one or two words. In this, you will give questions on different conditions and by applying the theorem you need to verify that whether the condition is correct or not, for example, if two sides of triangles are equal is the triangles similar or not.

Short Answer Type Questions-I

This section covers a total 11 questions in which you have to prove the triangles similar by applying the formulas and theorems or you have to find the third side or angle of the triangle by the given hints in the question.

Short Answer Type Questions-II

This section contains 24 questions in all where you have to verify that by the given set of conditions can we prove triangles similar. In this, you all have to make the figure by the details given in the statement.

Long Answer Type Questions

This section includes 18 questions in all and you have to prove the theorems in this section or you have applied the result of theorems on the questions. The questions are statement type questions and include all the theorems.

HOTS (Higher-Order Thinking Skills)

This section includes 7 questions in all which are a little bit tricky and confusing. In this type of questions, you have to identify which theorem is applied and have to solve questions according to that.

Value-Based Questions

This section contains 5 questions which are statement types in which you have to apply the proofs of theorems and identify the value which is used in the questions.

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