__CHAPTER 7 TRIANGLES__CONGRUENCY OF TRIANGLES

The symbol used to represent congruency of two triangles is ≅

1.

__SAS congruence rule__: Two triangles are congruent if two sides and the inclined angle of one triangle are equal to the sides and the included angle of the other triangle.

2.

__ASA congruence rule__: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.

3.

__AAS congruence rule:__Two triangles are congruent if any two pair of angles and one pair of corresponding sides are equal.

4.

__SSS congruence rule__: Two triangles are congruent if three sides of one triangle are equal to the three sides of another triangle.

5.

__RHS congruence rule__: Two triangles are congruent if in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle.

Theorems on triangles:

1. Angles opposite to equal sides of an isosceles triangle are equal.

2. The sides opposite to equal angles of triangle are equal.

3. If two sides of a triangle are unequal, the angle opposite to the longer side is larger.

4. In any triangle, the side opposite to the larger angle is longer.

5. The sum of any two sides of a triangle is greater than the third side