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11/07/2021 11:49 am
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Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of A (see Fig.). Show that:
(i) ΔAPB ΔAQB
(ii) BP = BQ or B is equidistant from the arms of A.
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11/07/2021 11:50 am
It is given that the line “l” is the bisector of angle A and the line segments BP and BQ are perpendiculars drawn from l.
(i) ΔAPB and ΔAQB are similar by AAS congruency because
P = Q (They are the two right angles)
AB = AB (It is the common arm)
BAP = BAQ (As line l is the bisector of angle A)
So, ΔAPB ΔAQB.
(ii) By the rule of CPCT, BP = BQ. So, it can be said the point B is equidistant from the arms of A.