If two triangles are congruent
they have equal sides, equal areas.

**Condition for Congruence**

__SAS Theorem:__If two sides and the angle between these two sides (included angle) of one triangle are congruent to the corresponding two sides and the included angle of a saecond triangle, then the two triangles are congruent

Example:

__AAS Theorem:__If two angles and a side not between these two angles of one triangle are congruent to two angles and the corresponding side not between these two angles of a second triangle, then the two triangles are congruent

**Example**:

__Hypotenuse-Leg Theorem:__If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and corresponding leg of a second right triangle, then the two triangles are congruent

**Example**:

__In a right angle triangle the square of the hypotenuse is equal to the sum of the squares of other two sides.__

**Pythagoras’ Theorem:**
b

^{2}=a^{2}+c^{2}__There are certain triplets which satisfy the pythagoras’ theorem and are commonly, called pythagorean triplet.__**Pythagorean**T**riplet**:**For example**:**3, 4, 5; 5, 12, 13; 24, 10, 26; 24, 7, 25; 15, 8, 17**__Appolonious Theorem:__
In triangle ABC, AD is median,
which divides BC into two equal parts. Then,

**AB**

^{2}+AC^{2}=2(AD^{2}+BD^{2})=2(AD^{2}+DC^{2})

__Stewart theorem:__
In Triangle ABC, AD divides side
BC in the ratio m and n. (Here AD need not be median) then,

**m.b**

^{2}+n.c^{2}=a(d^{2}+mn)

__Mean proportionality and Mid Point theorem:__
In the first triangle, DE // BC
so

**AD / DB = AE / EC**
In the second triangle, D and E
are mid points of AB and AC respectively. Which implies,

**AD / DB = AE / EC = 1**
Also,

**DE = 1 / 2 BC**