Page 198 - ICSE Math 7

X
3. In the adjoining figure, XO ⊥ YZ, OA ⊥ XY and OB ⊥ XZ. If OY = OZ, then
show that OA = OB.

A B

Y Z
O
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.]

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