| | | GEO0010 -- The fundamental principle of affine geometry |
Theorem. [The Fundamental Principle of Affine Geometry] Let A, B, and P be three points on a plane, and C be a point on line PA. The line passing through C and parallel to AB intersects PB in D. Q is the intersection of AD and BC. M is the intersection of AB and PQ. Show that M is the midpoint of AB.
point A 20 10
point B 70 10
point P 50 40
line ab A B
%line pa P A
line pb P B
online C P A
parallel pab C ab
intersec D pab pb
line ad A D
line bc B C
intersec Q ad bc
line pq P Q
intersec M ab pq
cmark_b A
cmark_b B
cmark_t P
cmark_t C
cmark_t D
cmark_r Q
cmark_b M
drawsegment A B
drawsegment A P
drawsegment A D
drawsegment B C
drawsegment B P
drawsegment C D
drawsegment P M
prove { equal { sratio A M M B } { 1 } }
| | | GEO0010 -- The fundamental principle of affine geometry |