ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

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Example – 1 : In the given figure, are two isosceles triangle on the same base BC. Show that the line PQ when produced bisects BC and is perpendicular to BC.

Solution : - Let PQ when produced meet BC at M.

And QB = QC Q is equidistant from B and C

Q lies on the perpendicular bisector of BC.

is the perpendicular bisector of BC.

Hence PQM bisector BC and is perpendicular to BC.

Example – 2 : In the adjoining figure, the bisector of of a quadrilateral ABCD intersect at a point P.

Show that P is a equidistant from the opposite sides BA and CD.

Solution : Let PM and PN be perpendicular to AB and CD respectively. PL is drawn perpendicular to BC.

P lies on the bisector of

Again P leis on the bisector of

From (i) and (ii) we get

PM = PN

Hence, P is equidistant from BA and CD.