Mind Map

Triangles of Class 9

  • Two figures are congruent if they are of the same shape and of the same size.
  • Two circles of same radii are congruent.
  • Two squares of same side are congruent.
  •  SAS congruence 
  • If two sides and the included angle of one triangle are equal to two sides and the included angle of other triangle then the two triangles are congruent.
  • ASA congruence:If two angles and the included side of one triangle are equal to two angles and the included side of other triangle, then the two triangles are congruent.
  • SSS congruence: If three sides of one triangle are equal to three sides of other triangle, then the two triangles are congruent.
  • RHS congruence:If in two right triangles hypotenuse and one side of one triangle are equal to the hypotenuse and one side of other triangle then the two triangles are congruent
  • AAS congruence:If two angles and one side of one triangle are equal to two angles and the corresponding side of other triangle, then the two triangles are congruent.
  •  Angles opposite to equal sides are equal. 
  • Sides opposite to equal angles are equal. 
  • Each angle of an equilateral triangle is 60°. 
  • In a triangle, angle opposite to longer side is greater. 
  • In a triangle, side opposite to the greater angle is longer. 
  • Sum of any two sides of a triangle is greater than the third side. 
  • Exterior angle is greater than either of the interior opposite angles.
  • If two triangles ABC and PQR are congruent under the correspondence A ↔ P, B ↔ Q, C ↔R, then symbolically it is expressed as ΔABC≅ΔPQR.
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