Triangle Congruence: ASA and AAS Answers

The SSS proof used the rigid transformations illustrated here. Which transformations are used?

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.