5) In the given figure AB = AC and AD is the bisector of   B A C   (a) Is A D B   A D C   ?   G i v e   r e a s o n s .   ( b )   I s   B = C give reasons.

(a) AB = AC ( Given )
∠ BAD= ∠ CAD ( DA is bisector of ∠ BAC)
AD=AD (common)
Hence, Triangle  ADB congurent to ADC(by SAS congurency rule)
(b) ∠B = ∠C (By CPCT)

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a) In triangle ADB and ACD
    AB=AC (as it is given)
    AD=AD (as it is common)
   ANGLE A (in triangle ADB ) = ANGLE A (in triangle ADC)  < as AD is a bisector of angle BAC>

 b) ANGLEB = ANGLE C because of the (CPCT rule of congruency of two congruent triangles)
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ab=ac (given)
ad=ad (common )
bd=cd (given)
hence abd is congruent to acd
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