What conclusion can be drawn from each part of Fig. 2.41, if

(a) DB is the bisector of ADC?



(b) BD bisects ABC?



(c) DC is the bisector of ADB, CA DA and CB DB?



a) Since, DB is the bisector of ADC.


This means that DB divides ADC into 2 equal parts.


ADB = BDC


b) Since, BD bisects ABC.


This means that, ABD = DBC.


c) Since, DC is the bisector of ADB


ADC = CDB ………….. (1)


Also, it is given that,


CAD = CBD = 90° ……….. (2)


Also, we know that sum of interior angles of a triangle is equal to 180°.


In Δ ACD,


ACD+ CDA+ DAC =180° …. (3)


In Δ BCD,


BCD+ CDB+ DBC =180° …. (4)


From (1), (2), (3), (4) we get,


ACD = BCD


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