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 (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)
if △ABC ∼ △DEF, then (distance BA) / (distance ED) = (distance CA) / (distance FD)
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance CA) / (distance FD)
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance BA) / (distance ED)
if △ABC ∼ △DEF, then (distance BC) / (distance EF) = (distance CA) / (distance FD)
if △ABC ∼ △DEF, then (distance ED) / (distance BA) = (distance DF) / (distance AC)
if △ABC ∼ △DEF, then (distance DF) / (distance AC) = (distance FE) / (distance CB)
if △ABC ∼ △DEF, then (distance FD) / (distance CA) = (distance EF) / (distance BC)
if △ABC ∼ △DEF, then (distance EF) / (distance BC) = (distance DE) / (distance AB)
if △ABC ∼ △DEF, then (distance EF) / (distance BC) = (distance DF) / (distance AC)
if △ABC ∼ △DEF, then △ACB ∼ △DFE
if △ABC ∼ △DEF, then △BCA ∼ △EFD
if △ABC ∼ △DEF, then △DEF ∼ △ABC
if (△ABC ∼ △DEF) and (△DEF ∼ △XYZ), then △ABC ∼ △XYZ
if (△ABC ∼ △DEF) and (△XYZ ∼ △DEF), then △ABC ∼ △XYZ
if △ABC ≅ △DEF, then △ABC ∼ △DEF
if (points A B and C are collinear) and (distance AC > distance BC), then m∠ABC = 180
if (m∠ABC = m∠CDA) and (m∠BCD = m∠DAB), then quadrilateral ABCD is convex
if ABCD is a rectangle, then quadrilateral ABCD is convex
if ABCD is a parallelogram, then quadrilateral ABCD is convex
if quadrilateral ABCD is convex, then point A lies in interior of ∠BCD
if quadrilateral ABCD is convex, then point B lies in interior of ∠CDA
if quadrilateral ABCD is convex, then point C lies in interior of ∠DAB
if ∠ABC is a right angle, then tangent of (m∠BCA) = (distance AB) / (distance BC)
if ∠ABC is a right angle, then sine of (m∠BCA) = (distance AB) / (distance AC)
if ∠ABC is a right angle, then cosine of (m∠BCA) = (distance BC) / (distance AC)
Pages:
19
20