Congruence Proofs

S: $$\Delta YOD\ \cong\ \Delta TOH$$  

R: ASA

S: $$\Delta YOD\ \cong\ \Delta TOH$$  

R: SAS 

S: $$\Delta YOD\cong\ \Delta TOH$$  

R: AAS

S: $$\Delta YOD\ \cong\ \Delta TOH$$  

R: SSS

S: $$\Delta YOD\cong\ \Delta TOH$$  

R: HL

S: $$\Delta TDP\ \cong\ \Delta ADP$$  

R: ASA

S: $$\Delta TDP\ \cong\ \Delta ADP$$  

R: SAS 

S: $$\Delta TDP\cong\ \Delta ADP$$  

R: AAS

S: $$\Delta TDP\ \cong\ \Delta ADP$$  

R: SSS

S: $$\Delta TDP\cong\ \Delta ADP$$  

R: HL

S: $$\angle2\ \cong\ \angle1$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle1\ \cong\ \angle4$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle2\ \cong\ \angle4$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle3\ \cong\ \angle1$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle3\ \cong\ \angle4$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle1\ \cong\ \angle4$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle2\ \cong\ \angle4$$  

R: Alt Int $$\angle$$  Thm

S: $$\angle3\ \cong\ \angle1$$  

R: Alt Int $$\angle$$  Thm

S: $$\Delta ZYX\ \cong\ \Delta XWZ$$  

R: ASA

S: $$\Delta ZYX\ \cong\ \Delta XWZ$$  

R: SAS 

S: $$\Delta ZYX\ \cong\ \Delta XWZ$$  

R: AAS

S: $$\Delta ZYX\ \cong\ \Delta XWZ$$  

R: SSS

S: $$\Delta ZYX\ \cong\ \Delta XWZ$$  

R: HL

S: $$\overline{BO}\ \cong\ \overline{BO}$$  

R: Reflexive PoC

S:   $$\overline{BH}\ \cong\ \overline{BC}$$  

R: Opp sides are $$\cong$$  

S: $$\overline{OH}\ \cong\ \overline{OC}$$  

R: Opp sides are $$\cong$$  

S: $$\overline{BO}\ \cong\ \overline{BO}$$  

R: Transitive PoC

S: $$\overline{DO}\ \cong\ \overline{HO}$$  

R: Def. of Segment Bisector

S:   $$\overline{YT}\ \cong\ \overline{DH}$$  

R: Opp sides are $$\cong$$  

S: $$\overline{OH}\ \cong\ \overline{OC}$$  

R: Given  

S:  

$$\overline{YO}\ \cong\ \overline{YO}$$  

R: Reflexive PoC

S: $$\overline{YO}\ \cong\ \overline{TO}$$  

R: Def. of Segment Bisector

S:   $$\overline{YT}\ \cong\ \overline{DH}$$  

R: Opp sides are $$\cong$$  

S: $$\overline{OH}\ \cong\ \overline{OC}$$  

R: Given  

S:  

$$\overline{YO}\ \cong\ \overline{YO}$$  

R: Reflexive PoC

S: $$\angle TDP\ \&\ \angle ADP\ are\ 90\degree$$  R: Def. of perpendicular

S: $$\angle TDP\ \&\ \angle ADP\ are\ 90\degree$$  R: Given 

S: $$\angle TDP\ \&\ \angle ADP\ are\ 180\degree$$  R: Def. of perpendicular

S: $$\angle D\ \cong\ \angle D$$  R: Reflexive PoC  

S: $$\overline{PD}\ \cong\ \overline{PD}$$  R: Reflexive PoC

S: $$\overline{TD}\ \cong\ \overline{AD}$$  R: Def of Segment Bisector

S: $$\overline{TP}\ \cong\ \overline{AP}$$  R: Opp. sides are $$\cong$$  

S: $$\angle PTD\ \cong\ \angle PAD$$  R: Alt. Int. Angle Thm.