| | | GEO0005 -- Pappus' Hexagon Theorem |
Theorem. [Pappus's Hexagon Theorem] If A, B, and C are three points on one line, A1, B1, and C1 are three points on another line, and AB1 meets BA1 at P, AC1 meets CA1 at Q, and BC1 meets CD1 at S, then the three points P, Q, and S are collinear.
point A 40 10
point B 90 10
%point C 120 10
online C A B
drawline A C
cmark_b A
cmark_b B
cmark_b C
point A_1 25 40
point B_1 45 45
%point C_1 65 50
online C_1 A_1 B_1
line A_1B_1 A_1 B_1
drawline A_1 C_1
cmark_t A_1
cmark_t B_1
cmark_t C_1
line AB_1 A B_1
line AC_1 A C_1
line BA_1 B A_1
line BC_1 B C_1
line CA_1 C A_1
line CB_1 C B_1
drawsegment A B_1
drawsegment A C_1
drawsegment B A_1
drawsegment B C_1
drawsegment C A_1
drawsegment C B_1
intersec P AB_1 BA_1
intersec Q AC_1 CA_1
intersec S BC_1 CB_1
cmark_l P
cmark_t Q
cmark_t S
color 255 0 0
drawline P S
prove { equal { signed_area3 P Q S } 0 }
| | | GEO0005 -- Pappus' Hexagon Theorem |