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Question
ΔPBC and ΔQBC are two isosceles triangles on the same base. Show that the line PQ is bisector of BC and is perpendicular to BC.
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Solution
Given: ΔPBC and ΔQBC are two isosceles triangles on the same base BC.
To prove: Line PQ is the perpendicular bisector of BC.
Proof: In ΔPBC, PB = PC
Since, the locus of a point equidistant from B and C is the perpendicular bisector of 1 of the line segment BC
∴ P lies on 1
Similarly Q lies on 1
Therefore, PQ is the perpendicular bisector of BC.
Hence proved.
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