1.

Construct a Delta ABC in which BC=6 cm, angleB=60^(@) and (AC-AB)=2 cm. Measure AC and AB. Justify your construction.

Answer»

SOLUTION :STEPS OF CONSTRUCTION
(i) Draw `BC=6` cm.
(ii) Construct `angle CBX=60^(@)`
(iii) Produce `XB` downwards to a POINT `X'`.
(iv) Set off `BD=2` cm along `BX'`.
(v) JOIN `CD`.
(vi) Draw the perpendicular bisector of `CD`, meeting `BX` at `A`.
(vii) Join `AC`.
Then, `Delta ABC` is the required triangle.
VERIFICATION :
On measuring, we FIND that `AC=5.4` cm and `AB=3.4` cm.
`:. (AC-AB)=(5.4-3.4)cm =2` cm.
Justification :
Since `A` lies on the perpendicular bisector of `CD`, we have `AD=AC`. Now, `BD=2` cm `implies AD-AB=2` cm
`implies AC-AB=2 cm ""[ :' AD=AC]`.
Hence, `Delta ABC` is the required triangle.


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