Page 198 - Start Up Mathematics_7

Group Activity

SSS Congruency and Rigidity of Triangles

Objective: To verify two triangles are congruent if three sides of a triangle are equal, respectively,
to the corresponding three sides of the other.
Material required: A packet of straws or broomsticks, ruler, a pair of scissors, gluestick or tape

Procedure: Students can arrange themselves in small groups of say 5 each. Each student of

the group should construct a triangle made up of straws or broomsticks whose corresponding
sides are equal to the sides of the triangles made by the other students of that group. To ensure
that the corresponding sides of the triangles are represented by straws of the same length, we
can hold the straws in a bunch and cut them with a pair of scissors. From the straws so cut
give one to each student of the group. Repeat the procedure to obtain more straws and join the

straws to form a triangle as shown.

Observation: Triangles so formed by students of the same group, if placed above each other
are found to be identical.

Result: Besides proving SSS congruency criterion one can verify that triangles are rigid,
i.e., the size and shape of triangles having the corresponding sides equal cannot be changed.
Note: Can you think of practical uses of rigidity of triangles?
[Hint: In bicycles, bridges, construction sites, etc.]

At a Glance

1. Two figures are said to be congruent if they have same shape and size.

2. Two line segments are said to be congruent iff they have the same length, i.e., AB ≅ CD iff
AB = CD.

3. Two angles are said to be congruent iff they have the same measure, i.e., ∠ABC ≅ ∠DEF
iff ∠ABC = ∠DEF.

4. Proving the congruency of plane figures by placing trace copy or cut-out of one figure on
the other is known as the method of superposition. We say that two figures are congruent if

they cover each other exactly, i.e., they are coincident.

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