RD Sharma Class 10 Chapter 4 (Triangles) Solutions

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The opening exercise of Chapter-4 RD Sharma Class 10 textbook introduces you with figures having the same shape but not necessarily the same size. Such shapes are said to have similar figures. Having understood the difference between congruent and similar shapes, you shall now proceed with studying the theorems.   

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Chapter 4 - Triangles

RD Sharma - MathematicsClass 10th , RD Sharma
Chapter 1 - Real Numbers
Chapter 2 - Polynomials
Chapter 3 - Pair of Linear Equations in Two Variables
Chapter 4 - Triangles
Chapter 5 - Trigonometric Ratios
Chapter 6 - Trigonometric Identities
Chapter 7 - Statistics
Chapter 8 - Quadratic Equations
Chapter 9 - Arithmetic Progressions
Chapter 10 - Circles
Chapter 11 - Constructions
Chapter 12 - Some Application of Trigonometry
Chapter 13 - Probability
Chapter 14 - Co-ordinate Geometry
Chapter 15 - Areas Related to Circles
Chapter 16 - Surface Areas and Volumes
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Class 10th RD Sharma

Important Theorems | RD Sharma Class 10 Chapter-4

Theorem 1: Line drawn parallel to one side of a triangle to intersect the other two sides in distinct points results in the division of the other two sides in the same ratio. 

Theorem 2: If a line is drawn intersecting any two sides of a triangle in the same ratio then the line will become parallel to the third side. 

Theorem 3: If there are two triangles with equal corresponding angles, then their corresponding sides will have the same ratio. These two triangles will be similar to each other. 

Theorem 4: If there are two triangles with sides having similar ratio then their corresponding angles will also be considered as equal. This way both the triangles will be similar. 

Theorem 5: If in two triangles, one angle of the first triangle is equal to one angle of the second triangle, then the two triangles are said to be similar. 

Theorem 6: The ratio of the areas of two triangles is equal to the square of the ratio of corresponding sides. 

Theorem 7: If you draw a perpendicular line from the vertex to the hypotenuse of a right-angled triangle, then both the triangles separated by the perpendicular are similar to each other and the whole triangle. 

Theorem 8: In a right-angled triangle, the square of the longest side is equal to the sum of the squares of the remaining two sides. 

Theorem 9: If in a triangle, the square of the longest side is equal to the sum of the squares of the remaining two sides, then the angle opposite the longest side is a right angle. 

Concepts in RD Sharma Class 10 Chapter-4

This chapter is wholly based on the application of different theorems of triangles that are used in accordance with the conditions. With a total of 9 theorems, you must first develop a better understanding about them from NCERT textbook before you proceed with the RD Sharma Class 10 questions. 

  1. Introduction
  2. Similar Figures
  3. Similarity of Triangles
  4. Criteria for Similarity of Triangles
  5. Areas of Similar Triangles
  6. Pythagoras Theorem