Page 45 - Mathematics Class - IX

ACTIVITY 4.2

OBJECTIVE

To verify experimentally the different criteria for congruency of triangles using triangle cut-outs.

MATERIALS REQUIRED

Cardboard

Scissors/cutter

White paper

Geometry box

Coloured glazed papers
Adhesive

PRE-REQUISITE KNOWLEDGE

1. Concept of congruency of triangles.
2. Different criteria for congruency of two triangles.

THEORY

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

2. Congruency of triangles: Two triangles are said to be congruent, if sides and angles of a triangle are equal
to the corresponding sides and angles of the other triangle.
3. Criteria for congruency of two triangles: There are four different criteria for the two triangles to be
congruent.

(i) SSS (Side-Side-Side) criterion: If three sides of one triangle are equal to the three sides of another
triangle, then the two triangles are said to be congruent.

(ii) SAS (Side-Angle-Side) criterion: Two triangles are said to be congruent, if two sides and the included
angle of a triangle are equal to the two sides and the included angle of the other triangle.
(iii) ASA (Angle-Side-Angle) criterion: Two triangles are said to be 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.

(iv) RHS (Right angle-Hypotenuse-Side) criterion: 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
said to be congruent.

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