Question 732383
1. Given: BD bisects AC, AB ≅ BC.
Prove: angle C ≅ angle A 


1.BD bisects AC, AB  &#8773 BC........given
2.AD &#8773CD.........................def. of bisector
3.BD &#8773BD.........................reflexive property
4. triangle ADB &#8773BDC.............SSS
5.angle C ≅ angle A......CPCTC


2. Given: BD is perpendicular to AC, AB ≅ BC.
Prove: angle CBD ≅ angle ABD 

1.BD is perpendicular to AC, AB ≅ BC.......given
2.angles ABD =angle BDC=90 ..............BD is perpendicular to AC
3. BD = BD............................ common
4. triangles ABD and CBD are &#877............ ASA
5. angle CBD ≅ angle ABD ..........RHS congruency