### Mathematics Class IX

Number Systems
Polynomials
Coordinate Geometry
Lines and Angles
Triangles
Circles
Constructions
Heron’s Formula
Surface Areas and Volumes
Statistics
Probability

# Criteria for Congruence of Triangles

#### SSS Criteria for Congruency

• If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
• If all sides are exactly the same, then their corresponding angles must also be exactly the same.

#### SAS Criteria for Congruency

Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

#### ASA Criteria for Congruency

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle

#### AAS Criteria for Congruency

Two triangles are said to be congruent to each other if two angles and one side of one triangle are equal to two angles and one side of the other triangle.

RHS Criteria for Congruency

• 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, then the two triangles are congruent.
• RHS stands for Right angle – Hypotenuse – Side.
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