**Important Concepts and Formulas**

1. Two figures are said to be congruent,
if they are of the same shape and of the same size.

2. Two circles are said to be congruent,
if they have the same radii.

3. Two squares are said to be congruent,
if they have the equal sides.

4. If two triangles PQR and ABC are
congruent under the correspondence P ↔
A, Q ↔ B and R ↔ C, then symbolically, it is expressed as ∆PQR ≅ ∆ABC.

5.

**Theorem 1:**Two triangles are congruent, if two sides and the included angled of one are respectively equal to the two sides and the included angle of the other. This is called SAS congruency condition.
6.

**Theorem 2:**Two triangles are congruent, if two angles and the included side of one are respectively equal to the two angles and the included side of the other. This is called ASA congruency condition.
7.

**Theorem 3:**Two triangles are congruent, if two angles and a side opposite to one angle of one triangle are respectively equal to the two angles and a side opposite to one angle of other triangle. This is called AAS congruency condition.
8.

**Theorem 4:**Two triangles are congruent, if the three sides of one triangle are respectively equal to the three sides of the other triangle. This is called SSS congruency condition.
9.

**Theorem 5:**Two right-angled triangles are congruent, if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other triangle. This is called RHS congruency condition.
10.

**Theorem 6:**Angles opposite to equal sides of a triangle are equal.
11.

**Theorem 7:**Sides opposite to equal angles of a triangle are equal.
12.

**Theorem 8:**In a triangle, angle opposite to the longer side is greater.
13.

**Theorem 9:**In a triangle, side opposite to the greater angle is longer.
14.

**Theorem 10:**Sum of any two sides of a triangle is greater than the third side.

To study the congruency of triangles in
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