QA-Tr-5: Parallelologic QA-Triple Triangles
Parallelologic pairs of Triple Triangles
Two triangles A1B1C1 and A2B2C2 are Parallelologic if the parallels from the vertices A1, B1, C1 wrt the sides B2C2, A2C2, and A2B2 are concurrent.
The point of concurrence is known as the Parallelologic Center of A1B1C1 with respect to A2B2C2.
If this is the case, then the parallels from the vertices A2, B2, C2 wrt the sides B1C1, A1C1, and A1B1 are also concurrent. The point of concurrence is known as the Parallelologic Center of A2B2C2 with respect to A1B1C1.
Here is a list of Parallelologic pairs of Triple Triangles in a Quadrangle.
| Triple Triangle-1 formed by 3 QA-versions of: |
Triple Triangle-2 formed by 3 QA-versions of: |
Parallelologic Center-1 | Parallelologic Center-2 |
|---|---|---|---|
| QG-P1 | QL-P8 | QA-Px | QA-P10 |
| QG-P2 | QL-P8 | QA-Px | QA-P10 |
| QG-P3 | QL-P5 | QA-Px | QA-Px |
| QG-P3 | QL-P15 | QA-Px | QA-Px |
| QG-P3 | QL-P18 | QA-Px | QA-Px |
| QG-P3 | QL-P28 | QA-Px | QA-Px |
| QG-P4 | QL-P8 | QA-Px | QA-P10 |
| QG-P5 | QG-P7 | QA-P3 | QA-P1 |
| QG-P5 | QG-P9 | QA-P3 | QA-P1 |
| QG-P5 | QL-P6 | QA-P3 | QA-Px |
| QG-P7 | QG-P10 | QA-P1 | QA-P2 |
| QG-P7 | QL-P2 | QA-P1 | QA-Px |
| QG-P8 | QL-P8 | QA-Px | QA-P10 |
| QG-P9 | QG-P10 | QA-P1 | QA-P2 |
| QG-P9 | QL-P2 | QA-P1 | QA-Px |
| QG-P10 | QL-P6 | QA-P2 | QA-Px |
| QG-P15 | QL-P8 | QA-Px | QA-P10 |
| QL-P2 | QL-P6 | QA-Px | QA-Px |
| QL-P4 | QL-P30 | QA-Px | QA-Px |
| QL-P5 | QL-P15 | QA-Px | QA-Px |
| QL-P5 | QL-P18 | QA-Px | QA-Px |
| QL-P8 | QL-P12 | QA-P10 | QA-Px |
| QL-P15 | QL-P18 | QA-Px | QA-Px |
QA-Px is a QA-point not registered in EQF.
Summary
- QA-P1 is the Parallelologic Center of the QG-P7 TT as well as the QG-P9 TT wrt the QG-P5/QG-P10/QL-P2 TT.
- QA-P2 is the Parallelologic Center of the QG-P10 TT wrt the QG-P7/QG-P9/QL-P6 TT.
- QA-P3 is the Parallelologic Center of the QG-P5 TT wrt the QG-P7/QG-P9/QL-P6 TT.
- QA-P10 is the Parallelologic Center of the QL-P8 TT wrt the QG-P1/QG-P2/QG-P4/QG-P8/QG-P15 TT.
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