|  |  | GEO0010 -- The fundamental principle of affine geometry

## GEO0010 -- The fundamental principle of affine geometry

##### The Theorem Statement [ZCG95]

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.

##### The Image - GCLC 5.0

##### Prover's Code

    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 }  }

##### Proved -- Proof, made with GCLC, v1.0

proofGEO0010.pdf

|  |  | GEO0010 -- The fundamental principle of affine geometry