Statements | Reasons |
1) DE || OQ | 1) Given (ΔPOQ) |
3) PE/EQ = PD/DO | 3) Basic Proportionality Theorem |
4) DF || OR | 4) Given (ΔPOR) |
5) PF/FR = PD/DO | 5)Basic Proportionality Theorem |
6) PE/EQ = PD/DO | 6) From (2) and (4) (Transitivity) |
7) EF || QR | 7) Converse of Basic Proportionality Theorem |
Statements | Reasons |
1) AB || PQ | 1) Given (ΔOPQ) |
3) OA/AP = OB/BQ | 3) Basic Proportionality Theorem |
4) AC || PR | 4) Given (ΔOPR) |
5) OA/AP = OC/CR | 5)Basic Proportionality Theorem |
6) OB/BQ = OC/CR | 6) From (2) and (4) (Transitivity) |
7) BC || QR | 7) Converse of Basic Proportionality Theorem |
Statements | Reasons |
1) DE || BC | 1) Given (ΔABC) |
3) AB/AD = AC/AE | 3) Basic Proportionality Theorem |
4) FE || DC | 4) Given (ΔADC) |
5) AD/AF = AC/AE | 5)Basic Proportionality Theorem |
6) AB/AD = AD/AF | 6) From (2) and (4) (Transitivity) |
7) AD^{2} = AB x AF | 7) Cross multiply |