TRIANGLE CBSC CLASS 10TH

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6. Triangles (1.See Thales Theorem ) 

Similar Figures 2.Similar Figures  

Figures which have the same shape but not necessarily the same size are called similar (symbol: ).  \\Congruency can be understood as a special case of similarity where the size of the shapes is also equal. Thus, all congruent figures are similar, but all similar figures need not to be congruent 

Similar Triangles  (Similarity of Triangles )

Basic Proportionality Theorem or Thales Theorem () 

Converse of Basic Proportionality Theorem or Thales Theorem  

Equiangular Triangles(Equiangular Triangles )  

AAA Similarity  

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

  {Converse of AAA Similarity Theorem} 

 If three sides of a triangle are proportional to the corresponding sides of another Triangles then corresponding angles are  also equal. 

Simulation

AA Similarity (Based on AAA Similarity ) 3. (See Areas of Triangles )

AA SimilaritySee (Based on AAA Similarity)  

You know that if two angles of a triangle are equal to two angles of another triangle, then by the angle sum property, the third angle will also be equal.  Thus, by the AAA similarity criterion, if two angles of a triangle are equal to the two corresponding angles of another triangle.  

SSS SimilaritySee 

 

SAS Similarity  See

Relationship Between the Ratios of Areas and Corresponding Sides  See

Pythagoras Theorem4.(See Pythagoras Theorem )

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