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Question 3
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 75 of the corresponding sides of the first triangle.


Solution

Steps of Construction:
Step I:A triangle ABC with sides 5 cm, 6 cm and 7 cm is drawn.
Step II:A ray BX making an acute angle with BC is drawn opposite to vertex A.
Step III:7 points, B1,B2,B3,B4,B5,B6andB7 are marked on BX.
Step IV;Point B5 is joined with C to draw B5C.

Step V: B7C' is drawn parallel to B5C and C'A' is parallel to CA.
Thus A'BC' is the required triangle.

Justification
ΔABC ΔABC by AAA similarity condition
ABAB=ACAC=BCBC
and BCBC=BB5BB7=57
ABAB=ACAC=BCBC=75

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