MP Board Book for Class 10th Mathematics Chapter 6- Triangles

In this we will discuss the particular chapter 6- triangles. In this chapter we will discuss the definition of triangle, properties of triangle, proof of the property, examples of sums, questions according to what we have  learnt in this chapter. We will learn about these properties-

Properties-

• If a line is drawn parallel to one side of a triangle to intersect the other two points in a distinct side are divided in the same ratio.
• If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third ratio.
• If in two triangles, corresponding angles are equal, then their corresponding angles are in the same ratio and hence the two triangles are similar.
• If in two triangles, sides of one triangle are proportionate to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.
• If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.
• The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding angles.
• If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles of both the sides of the perpendicular are similar to the whole triangle and to each other.
• In a triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
•  In a triangle if the square of one side is equal to the sum of squares of the other two sides then the angle opposite to the first side is right angle.