Function Parallel Lines

lines AB and CD are parallel

Format:

AB || CD

Input:

Output:

Details:

Conditional properties that reference this function:

• if AB || CD, then point C lies in interior of ∠ABD (link)
• if m∠CDE = m∠CAB, then DE || AB (link)
• if (AB || CD) and (∠ABD is a right angle), then ∠BDC is a right angle (link)
• if AB || CD, then BA || DC (link)
• if AB || CD, then CD || AB (link)
• if (AB || YZ) and (m∠ABC = 180), then BC || YZ (link)
• if (AB || YZ) and (m∠AXB = 180), then AX || YZ (link)
• if (AB || YZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AC || XZ (link)
• if (AB || XY) and (m∠ABC = 180) and (m∠XYZ = 180), then AC || XZ (link)
• if (AC || XZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AB || YZ (link)
• if (AC || XZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AB || XY (link)
• if (AB || CD) and (m∠AXB = 180) and (m∠CYD = 180), then XB || CY (link)
• if (AB || CD) and (m∠AXY = 180) and (m∠XYB = 180), then XY || CD (link)
• if AB || CD, then not(line AB intersects line CD) (link)
• if AB || CD, then (m∠BAC) + (m∠ACD) = 180 (link)
• if (m∠BAC) + (m∠ACD) = 180, then AB || CD (link)
• if (m∠DBA) + (m∠CDB) = 180, then AB || CD (link)
• if (AB || CD) and (line AB intersects line EF at point X), then line EF intersects line CD at point Z (link)
• if (AB || CD) and (AC || BD), then ABDC is a parallelogram (link)
• if ABCD is a parallelogram, then AB || DC (link)
• if ABCD is a parallelogram, then AD || BC (link)
• if quadrilateral ABCD is an isosceles trapezoid, then AB || DC (link)
• if quadrilateral ABCD is a trapezoid, then AB || DC (link)
• if slope of line AB = slope of line CD, then AB || CD (link)

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