1.

Construct a Delta ABC in which BC=6 cm, angleB=60^(@) and (AB+AC)=9 cm. Measure AB andAC. Justify your answer.

Answer»

Solution :STEPS OF CONSTRUCTION
(i) Draw `BC=6` CM.
(ii) Construct `angleCBX=60^(@)`.
(iii) Along `BX`, set off `BP=9` cm.
(iv) Join CP.
(v) Draw the perpendicular BISECTOR of CP to intersect BP at A.
(vi) Join AC.
Then, `Delta ABC` is the required triangle.
Verification :
On measuring, we find that
`AB+AC=(4+5)` cm `=9` cm.
Justification :
Clearly, A lies on the perpendicular bisector of CP.
`:. AP=AC`.
Now, `BP=9` cm [SEE Step (iii)]
`implies AB+AP=9` cm
`implies AB+AC=9 cm""[ :' AP=AC]`.
Hence, `DeltaABC` is the required triangle.


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