Similarity

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Introduction

     Triangles are similar if they are equiangular and their corresponding sides are proportional.

Similarity

     Two triangles are similar if (i) Their angles are the same and, (ii) he corresponding sides are proportional.

Enlargement or Dilatation

    The corresponding sides are parallel to each other.

Theorem1 (S.A.S) Similarity

    If a pair of corresponding angles are equal and the sides including them are proportional, then the triangles are similar.

Theorem2 (A.A) Similarity

    If two pairs of corresponding angles are equal, then the triangles are similar.

Theorem3 (S.S.S) Similarity

    If three pairs of corresponding sides are proportional then the two triangles are similar.

Theorem4

    A perpendicular drawn from the right angle vertex of a right - angled triangle divides the triangle into two triangles similar to each other and also to the original triangle.

Summary

     (S.S.S Similarity) : If three pairs of corresponding sides are proportional, then the two triangles are similar.

Question and Answers

Question and Answers 1