# Triangles Class 10 Notes Maths Chapter 6

#### CHAPTER AT A GLANCE

##### Similar Figures

Two figures having the same shape but not necessarily the same size are called similar figures/
Two figures having the same shape as well as same size are called congruent figures.

Note : that all congruent figures are similar but the similar figures need not be congruent.

##### Similarity of Triangles

Two triangles are similar, if
(i) their corresponding angles are equal and
(ii) their corresponding sides are in the same ratio (or proportion)

NOTE : If corresponding angles of two triangles are equal, then they are known as

##### Equiangular Triangles.

Criteria for Similarity of Triangles

(i) AAA Similarity Criterion : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

(ii) AA Similarity Criterion : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

(iii) SSS Similarity Criterion : If in two triangles, corresponding sides are in the same ratio then their correspoding angles are equal and hence the triangles are similar.

(iv) SAS Similarity Criterion : If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportion), then the two triangles are similar.

##### Theorems and some Important Results

Theorem : Basic Proportionality Theorem or Thale’s Theorem
Statement: “If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio”
In ABC, a line parallel to BC intersects AB at D and AC at E. then

Theorem: Converse of B.P. Theorem

Statement: “If a line divides any two sides of a triangle in the same ratio,”

##### Areas of Two Similar Triangles

Theorem 1: Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Theorem 2: Prove that the areas of two similar triangles are in the ratio of the square of corresponding altitudes.

Theorem: Pythagoras Theorem or Bodhayan Theorem

Statement: Prove that,”In a right angled triangle, the square of the hypotenuse is equal to the sum of the other two sides”.

Theorem: Converse of Pythagoras Theorem

Statement: “In a triangle, the square of the longer side is equal to the sum of the squares of the other two sides then the triangle is right angled triangle”.
ABC is a triangle such that BC2 = AB2 + AC2 then LA = 90Â°

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