Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii) SSS (iv) RHS AAS criterion for congruence of triangles as a particular case of ASA criterion.
• Angles opposite to equal sides of a triangle are equal,
• Sides opposite to equal angles of a triangle are equal,
• A point equidistant from two given points lies on the perpendicular bisector of the line-segment joining the two points and its converse,
• A point equidistant from two intersecting lines lies on the bisectors of the angles formed by the two lines,
• In a triangle
(i) side opposite to the greater angle is longer
(ii) angle opposite the longer side is greater
(iii) the sum of any two sides is greater than the third side.