Conditional Properties
In each statement, if the test expression is true, then the conclusion expression is also assumed to be true. Conditional properties are used to prove theorems.
if m∠ABC = 90, then ∠ABC is a right angle
if (△XYZ is a triangle) and (segment XY ≅ segment YZ), then △XYZ is an isosceles triangle
if ray BD bisects ∠ABC, then m∠ABD = m∠DBC
if m∠ABD = m∠DBC, then ray BD bisects ∠ABC
if ray BD bisects ∠ABC, then m∠DBC = (m∠ABC) / 2
if (ray BD bisects ∠ABC) and (m∠BPD = 180) and (PM ⊥ MB) and (PN ⊥ NB), then distance PM = distance PN
if (distance PM = distance PN) and (PM ⊥ MB) and (PN ⊥ NB), then ray BP bisects ∠ABC
if (∠ABC is an acute angle) and (∠BCA is an acute angle) and (∠CAB is an acute angle), then △ABC is an acute triangle
if ∠ABC is an acute angle, then m∠ABC < 90
if m∠ABC = 180, then (distance AB) + (distance BC) = distance AC
if m∠ABC = 180, then m∠BCX = m∠ACX
if m∠ABC = 180, then m∠ABC = (m∠ABX) + (m∠XBC)
if M is the midpoint of line AB, then distance AM = distance MB
if (distance AM = distance MB) and (m∠AMB = 180), then M is the midpoint of line AB
if M is the midpoint of line AB, then m∠AMB = 180
if M is the midpoint of line AB, then the x coordinate of point M = ((the x coordinate of point A) + (the x coordinate of point B)) / 2
if M is the midpoint of line AB, then the y coordinate of point M = ((the y coordinate of point A) + (the y coordinate of point B)) / 2
if ∠ABC and ∠DEF are complementary, then (m∠ABC) + (m∠DEF) = 90
if ∠ABC and ∠DEF are supplementary, then (m∠ABC) + (m∠DEF) = 180
if (m∠ABC) + (m∠DEF) = 180, then ∠ABC and ∠DEF are supplementary
if m∠CDE = m∠CAB, then DE || AB
if (AB || CD) and (∠ABD is a right angle), then ∠BDC is a right angle
if AB || CD, then BA || DC
if AB || CD, then CD || AB
if (AB || YZ) and (m∠ABC = 180), then BC || YZ
if (AB || YZ) and (m∠AXB = 180), then AX || YZ
if (AB || YZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AC || XZ
if (AB || XY) and (m∠ABC = 180) and (m∠XYZ = 180), then AC || XZ
if (AC || XZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AB || YZ
if (AC || XZ) and (m∠ABC = 180) and (m∠XYZ = 180), then AB || XY
if (AB || CD) and (m∠AXB = 180) and (m∠CYD = 180), then XB || CY
if (AB || CD) and (m∠AXY = 180) and (m∠XYB = 180), then XY || CD
if ABCD is a square, then ABCD is a rectangle
if ABCD is a square, then distance AB = distance BC
if (ABCD is a rectangle) and (distance AB = distance BC), then ABCD is a square
if m∠abc = 90, then area of △ABC = (((distance AB) ⋅ (distance BC)) ⋅ 1) / 2
if AB || CD, then not(line AB intersects line CD)
if AB || CD, then (m∠BAC) + (m∠ACD) = 180
if (m∠BAC) + (m∠ACD) = 180, then AB || CD
if (m∠DBA) + (m∠CDB) = 180, then AB || CD
if △ABC ≅ △DEF, then area of △ABC = area of △DEF
if △ABC ≅ △DEF, then △BCA ≅ △EFD
if △ABC ≅ △DEF, then △BAC ≅ △EDF
if △ABC ≅ △DEF, then △DEF ≅ △ABC
if (△ABC ≅ △DEF) and (△DEF ≅ △GHI), then △ABC ≅ △GHI
if (distance AB = distance DE) and (m∠ABC = m∠DEF) and (distance BC = distance EF), then area of △ABC = area of △DEF
if (distance AB = distance DE) and (m∠ABC = m∠DEF) and (distance BC = distance EF), then △ABC ≅ △DEF
if (m∠ABC = m∠DEF) and (distance BC = distance EF) and (m∠BCA = m∠EFD), then △ABC ≅ △DEF
if (distance AB = distance DE) and (distance BC = distance EF) and (distance CA = distance FD), then △ABC ≅ △DEF
if (m∠ABC = m∠DEF) and (distance BC = distance EF) and (m∠BCA = m∠EFD), then area of △ABC = area of △DEF
if △ABC ≅ △DEF, then m∠ABC = m∠DEF
if △ABC ≅ △DEF, then m∠CAB = m∠FDE
if △ABC ≅ △DEF, then m∠BCA = m∠EFD
if △ABC ≅ △DEF, then distance AB = distance DE
if △ABC ≅ △DEF, then distance BC = distance EF
if △ABC ≅ △DEF, then distance CA = distance FD
if (distance AB = distance BC) and (distance BC = distance CD) and (distance CD = distance DA) and (m∠ABC = 90), then ABCD is a square
if ABCD is a square, then area of quadrilateral ABCD = (distance AB) ⋅ (distance AB)
if m∠ABC = 180, then area of △ACD = area of quadrilateral ABCD
if m∠ABC = 180, then area of quadrilateral XABC = area of △XAC
if m∠ABC = 180, then area of pentagon ACDEF = area of hexagon ABCDEF
if m∠DEF = 180, then area of hexagon ABCDEF = area of pentagon ABCDF
if (m∠ABC = 90) and (m∠DEF = 180), then m∠ABC < m∠DEF
if line AB intersects line CD at point X, then m∠AXB = 180
if line AB intersects line CD at point X, then m∠CXD = 180
if (m∠ABD = 180) and (m∠ACD = 180), then m∠ABC = 180
if (m∠ABD = 180) and (m∠ACD = 180), then m∠BCD = 180
if (m∠ABC = 180) and (m∠BCD = 180), then m∠ABD = 180
if (m∠ABC = 180) and (m∠BCD = 180), then m∠ACD = 180
if (AB || CD) and (line AB intersects line EF at point X), then line EF intersects line CD at point Z
if (AB || CD) and (AC || BD), then ABDC is a parallelogram
if ABCD is a parallelogram, then AB || DC
if ABCD is a parallelogram, then AD || BC
if ABCD is a rectangle, then ABCD is a parallelogram
if ABCD is a rectangle, then ∠ABC is a right angle
if (ABCD is a parallelogram) and (∠ABC is a right angle), then ABCD is a rectangle
if (ABCD is a parallelogram) and (∠CDA is a right angle), then ABCD is a rectangle
if ABCD is a rhombus, then ABCD is a parallelogram
if ABCD is a rhombus, then distance AB = distance BC
if (ABCD is a parallelogram) and (distance AB = distance BC), then ABCD is a rhombus
if (ABCD is a parallelogram) and (distance CD = distance DA), then ABCD is a rhombus
if (ABCD is a parallelogram) and (distance DA = distance AB), then ABCD is a rhombus
if (m∠ABC = m∠BCA) and (m∠BCA = m∠CAB), then △ABC is an equilateral triangle
if △ABC is an equilateral triangle, then distance AB = distance BC
if △ABC is an equilateral triangle, then distance AB = distance AC
if (distance AB = distance BC) and (distance BC = distance CA), then △ABC is an equilateral triangle
if quadrilateral ABCD is an isosceles trapezoid, then AB || DC
if quadrilateral ABCD is an isosceles trapezoid, then distance AD = distance BC
if quadrilateral ABCD is a trapezoid, then AB || DC
if slope of line AB = slope of line CD, then AB || CD
if slope of line AB = 0, then distance AB = (the x coordinate of point B) - (the x coordinate of point A)
if (m∠ABC = m∠DEF) and (m∠BCA = m∠EFD) and (m∠CAB = m∠FDE) and ((distance AB) / (distance DE) = (distance BC) / (distance EF)) and ((distance BC) / (distance EF) = (distance CA) / (distance FD)), then △ABC ∼ △DEF
if △ABC ∼ △DEF, then m∠ABC = m∠DEF
if △ABC ∼ △DEF, then m∠BCA = m∠EFD
if △ABC ∼ △DEF, then m∠CAB = m∠FDE
if △ABC ∼ △DEF, then (distance CB) / (distance FE) = (distance CA) / (distance FD)
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance BC) / (distance EF)
if △ABC ∼ △DEF, then (distance AC) / (distance DF) = (distance AB) / (distance DE)
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance AB) / (distance DE)
if △ABC ∼ △DEF, then (distance AB) / (distance DE) = (distance BC) / (distance EF)