Math III
SSS, SAS, & HL Proofs
1)
Name: ________________________
Given: B is the midpoint of AE
B is the midpoint of CD
Prove: ∆ABD  ∆EBC
Statement
Reason
1. B is the midpoint of AE
1. Given
B is the midpoint of CD
2. AB  BE , CB  BD
3. ABD  EBC
4. ∆ABD  ∆EBC
2)
2. Definition of Midpoint
3. Vertical Angle Congruence Theorem
4. SAS Congruence Postulate
Given: AB  CD, BC  AD
Prove: ∆ABC  ∆CDA
Statement
Reason
1. AB  CD, BC  AD
1. Given
2. AC  AC
3. ∆ABC  ∆CDA
2. Reflexive Property of Congruence
3. SSS Congruence Postulate
3)
Given: AB  CD, AB || CD
Prove: ∆ABC  ∆DCB
Statement
Reason
1. AB  CD, AB || CD
2. ABC  DCB
3. CB  CB
4. ∆ABC  ∆DCB
1. Given
2. Alternate Interior Angles Theorem
3. Reflexive Property of Congruence
4. SAS Congruence Postulate
4)
Given: QS  PR, PS  RS , QR  RS
Prove: ∆PRS  ∆QSR
Statement
Reason
1. QS  PR, PS  RS , QR  RS
2. PSR and SRQ are right angles
3. ∆PRS and ∆QSR are right triangles.
4. RS  RS
5. ∆PRS  ∆QSR
1. Given
2. Definition of Perpendicular Lines
3. Definition of Right Triangles
4. Reflexive Property of Congruence
5. HL Congruence Theorem
5)
Given: OM  LN , ML  MN
Prove: ∆OML  ∆OMN
Statement
Reason
1. OM  LN , ML  MN
2. OML and OMN are right angles
3. OML  OMN
4. OM  OM
5. ∆OML  ∆OMN
1. Given
2. Definition of Perpendicular Lines
3. Right Angle Congruence Theorem
4. Reflexive Property of Congruence
5. SAS Congruence Postulate
6)
Given: AB  CB
D is the midpoint of AC
Prove: ∆ABD  ∆CBD
Statement
Reason
1. AB  CB
1. Given
D is the midpoint of AC
2. AD  CD
2. Definition of Midpoint
3. BD  BD
4. ∆ABD  ∆CBD
3. Reflexive Property of Congruence
4. SSS Congruence Postulate