|  |  | GEO0009 -- Midpoint of a Parallelogram

## GEO0009 -- Midpoint of a Parallelogram

##### The Theorem Statement [ZCG95]

Theorem. Let O be the intersection of the two diagonals AC and BD of a parallelogram ABCD. Then O is the midpoint of AC.

##### The Image - GCLC 5.0

##### Prover's Code

    point A 20 10
    point B 70 10
    point C 90 40

    line ab A B
    parallel cd C ab

    line bc B C
    parallel ad A bc

    intersec D ad cd

    line a A C
    line b D B

    intersec O a b

    drawsegment A B
    drawsegment A D
    drawsegment D C
    drawsegment B C
    drawsegment A C
    drawsegment B D

    cmark_b A
    cmark_b B
    cmark_t C
    cmark_t D
    cmark_b O

    prove { equal { sratio A O O C } { 1 }  }

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

proofGEO0009.pdf

|  |  | GEO0009 -- Midpoint of a Parallelogram