|  |  | GEO0006 -- Menelaus' Theorem

## GEO0006 -- Menelaus' Theorem

##### The Theorem Statement[CGZ96]

Theorem. [Menelaus' Theorem] A transversal meets the three sides AB, BC, and CA of a triangle ABC in F, D, and E respectively. Then (AF)/(FB) = - (DC)/(BD) × (EA)/(CE). The non-degenerate condition is that A, B, and C are not on line EF.

##### The Image - GCLC 5.0

##### Prover's Code

    dim 100 100
    area 5 5 90 90

    point A 30 20
    point B 70 20
    point C 40 70

    point X 15 55
    point Y 75 10

    line a B C
    line b A C
    line c A B

    line p X Y

    intersec D a p
    intersec E b p
    intersec F c p

    drawsegment A B
    drawsegment A C
    drawsegment B C

    drawline p

    cmark_b A
    cmark_t B
    cmark_t C

    cmark_t D
    cmark_lt E
    cmark_rt F

    prove { equal { signed_area3 D E F } { 0 } }

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

proofGEO0006.pdf

|  |  | GEO0006 -- Menelaus' Theorem