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TOPICS
Introduction

Introduction of Triangle

A polygon with three edges, three vertices and no. of three angles is called Trangle. In this figure,
(i) AB, BC and AC are three Edges.
(ii) Point A, B and C are three Vetices.
(iii) ∠1, ∠2 and ∠3 are three Angles.

Similar Figures

Two figures having the same shape but not necessarily the same size are called Similar Figures.

Congruent Figures

Two figures having the same shape and the same size are called Congruent Figures.
Note : All the congruent figures are similar but the similar figures are not congruent.

Similarity of Triangles (AAA Similarity of Triangles)

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

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.

SSS similarity criterion

If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar.

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 (proportional), then the triangles are similar.

Areas of Similar Triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Pythagoras Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). In this triangle, one angle is always 90 degree.

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