RS Aggarwal Solutions Class 7 Chapter-15 Properties of Triangles (Ex 15D) Exercise 15.4

There are basically six types of triangles. They are as follows:

Set 1 type according to the length of the sides 

• Scalene triangle having no equal sides

• Isosceles triangle having two equal sides

• Equilateral triangle having all three equal sides

Set 2 type according to the measure of the internal angles

• Acute triangle having all three interior angles less than 90 degrees

• Obtuse triangle having one angle greater than 90 degrees in measure.

• Right triangle having one angle equal to 90 degrees in measure.

Now the scalene and isosceles of the first set of triangles can have three subtypes of set 2 i.e. acute, obtuse and right angled type. In that way altogether there can be 12 types of triangles.

The conditions for two triangles to be congruent are as follows:

• Lengths of any two sides of the triangle and the angle formed by those two lines will exactly be equal to the Lengths of any two sides of the triangle and the angle formed by those two lines of the other triangle

• The measure of the two internal angles and the length of the side included in forming the two angles should be equal to the measure of the two internal angles and the length of the side included in forming the two angles of the other triangle.

• The length of the hypotenuse and the length of any leg of one right angled triangle should be equal to the length of the hypotenuse and the length of any one leg of another right-angled triangle.

• The length of the hypotenuse and the measure of anyone acute angle of one right angled triangle should be equal to the length of the hypotenuse and the measure of anyone acute angle of another right-angled triangle.

Triangle is the first basic shape in the world of geometry. The students should learn triangles from elementary classes to recognize shapes. Class 7 is the ideal class to study the properties of triangles because the other polygonal concepts are based on the knowledge of the simplest form of a polygon. In fact, all other polygons can be broken into triangles. Not only this, some of the real-life examples of triangles told the significance of this chapter at the school level. To understand the traffic signals, the shape of the temples and pyramids, boats, monuments and to measure the height of a mountain the concept of triangles is needed. Scoring well in Trigonometry in higher classes also depends upon the clarity of the concepts of triangles.

NCERT books are always the first book to be studied for a CBSE student of any standard. However for further practice and strengthening their concepts they should go for RS Aggarwal or RD Sharma. This particular topic Properties of Triangles is well illustrated in Chapter 15 of RS Aggarwal, for easy and steady learning. This book will help to gradually grow and strengthen your concepts on properties of triangles which will be quite helpful in higher classes even. To make your study even easier, Vedantu has taken the effort of providing you the PDF versions of Chapter 15 of RS Aggarwal along with RS Aggarwal Solutions Class 7 Chapter-15 Properties of Triangles (Ex 15D). Solutions of Exercise 15.4 have been prepared by Maths experts in Vedantu and they are available in free PDF versions on the website. Students can download them whenever needed.