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Question 4
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1.5 times the corresponding sides of the isosceles triangle.

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Solution

Steps of Construction:
Step I: BC = 8 cm is drawn.
Step II: Perpendicular bisector of BC is drawn and it intersects BC at O.


Step III: At a distance of 4 cm, a point A is marked on the perpendicular bisector of BC.

Step IV: AB and AC are joined to form ΔABC.
Step V: A ray BX is drawn making an acute angle with BC opposite to vertex A.
Step VI: 3 points B1,B2andB3 are marked on BX.
Step VII: B2 is joined with C to form B2C.
Step VIII: B3C is drawn parallel to B2C and C'A' is drawn parallel to CA.
Thus, A'BC' is the required triangle formed.

Justification:
ΔABC ~ ΔABC by AA similarity condition.

ABAB=BCBC=ACAC
Also,
ABAB=AA2AA3=23

AB=32AB,BC=32
BC and AC=32AC

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