Gary is using an indirect method to prove that segment de is not parallel to segment bc in the triangle abc shown.. he starts with the assumption that segment de is parallel to segment bc.. which inequality will he use to contradict the assumption? . 4: 10 ≠ 6: 14. 4: 6 ≠ 6: 14. 4: 10 ≠ 6: 8. 4: 14 ≠ 6: 10

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)