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.

Similar Angles Property
if △ABC ∼ △DEF, then m∠ABC = m∠DEF

Similar Angles Property 2
if △ABC ∼ △DEF, then m∠BCA = m∠EFD

Similar Angles Property 3
if △ABC ∼ △DEF, then m∠CAB = m∠FDE

Proportions in Similar Triangles
if △ABC ∼ △DEF, then (distance CB) / (distance FE) = (distance CA) / (distance FD)

Proportions in Similar Triangles 2
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance BC) / (distance EF)

Proportions in Similar Triangles 3
if △ABC ∼ △DEF, then (distance AC) / (distance DF) = (distance AB) / (distance DE)

Proportions in Similar Triangles 4
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance AB) / (distance DE)

Proportions in Similar Triangles 5
if △ABC ∼ △DEF, then (distance AB) / (distance DE) = (distance BC) / (distance EF)

Proportions in Similar Triangles 6
if △ABC ∼ △DEF, then (distance BA) / (distance ED) = (distance CA) / (distance FD)

Proportions in Similar Triangles 7
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance CA) / (distance FD)

Proportions in Similar Triangles 8
if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance BA) / (distance ED)

Proportions in Similar Triangles 9
if △ABC ∼ △DEF, then (distance BC) / (distance EF) = (distance CA) / (distance FD)

155
if △ABC ∼ △DEF, then (distance ED) / (distance BA) = (distance DF) / (distance AC)

156
if △ABC ∼ △DEF, then (distance DF) / (distance AC) = (distance FE) / (distance CB)

157
if △ABC ∼ △DEF, then (distance FD) / (distance CA) = (distance EF) / (distance BC)

158
if △ABC ∼ △DEF, then (distance EF) / (distance BC) = (distance DE) / (distance AB)

159
if △ABC ∼ △DEF, then (distance EF) / (distance BC) = (distance DF) / (distance AC)

1517
if △ABC ∼ △DEF, then △ACB ∼ △DFE

Similar Triangles
if △ABC ∼ △DEF, then △BCA ∼ △EFD

Symmetric Property of Similar Triangles
if △ABC ∼ △DEF, then △DEF ∼ △ABC

Transitive Property of Similar Triangles
if (△ABC ∼ △DEF) and (△DEF ∼ △XYZ), then △ABC ∼ △XYZ

1521
if (△ABC ∼ △DEF) and (△XYZ ∼ △DEF), then △ABC ∼ △XYZ

Congruent Triangels are Similar
if △ABC ≅ △DEF, then △ABC ∼ △DEF

If Collinear Then Angle is 180
if (points A B and C are collinear) and (distance AC > distance BC), then m∠ABC = 180

If Opposite Angles Are Equal Then Quad is Convex
if (m∠ABC = m∠CDA) and (m∠BCD = m∠DAB), then quadrilateral ABCD is convex

Rectangles Are Convex
if ABCD is a rectangle, then quadrilateral ABCD is convex

Parallelograms Are Convex
if ABCD is a parallelogram, then quadrilateral ABCD is convex

Convex Quadrilateral
if quadrilateral ABCD is convex, then point A lies in interior of ∠BCD

Convex Quadrilateral 2
if quadrilateral ABCD is convex, then point B lies in interior of ∠CDA

Convex Quadrilateral 3
if quadrilateral ABCD is convex, then point C lies in interior of ∠DAB

Definition of Tangent
if ∠ABC is a right angle, then tangent of (m∠BCA) = (distance AB) / (distance BC)

Definition of Sine
if ∠ABC is a right angle, then sine of (m∠BCA) = (distance AB) / (distance AC)

Definition of Cosine
if ∠ABC is a right angle, then cosine of (m∠BCA) = (distance BC) / (distance AC)

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