# 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.