Congruence of Triangles
* Two triangles are congruent, if the sides and angles one triangle are equal to corresponding sides and angles of the other triangle.
* There is one-to-one correspondence between the vertices f two congruent triangles
ABC and XYZ such that A ↔ X, B ↔ Y and C ↔ Z.
* Two triangles are congruent, if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle. Its referred as Side-Angle-Side (SAS) congruence rule.
* Two triangles are congruent, if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle. It is referred as Angle-Side-Angle (ASA) congruence rule.
* Two triangles are congruent, if three sides of one triangle are equal to three sides of the other triangle. This is referred as Side-Side-Side (SSS) congruence rule.
* Two right-angled triangles are congruent, if the hypotenuse and a side one triangle are equal to the hypotenuse and the corresponding side of the other triangle. This is referred as Right angle-Hypotenuse-Side (RHS) congruence rule.
Important Properties of Triangles:
* Angles opposite to equal sides of an isosceles triangle are equal.
* Sides opposite to the equal angles of a triangle are equal.
* The three angles of an equilateral triangle are equal.
Inequalities In A Triangle
Theorem 1: If two sides of a triangle are unequal, the angle opposite to the longer side is larger.
Theorem 2: In any triangle, the side opposite to the larger angle is lager.
Theorem 3: The sum of any two sides of a triangle is greater than the third side.