Transitive Property of Equality Variation 2
Angle Symmetry Example 2
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Angle Symmetry Example
Transitive Property of Equality Variation 1
Right Angles are Equal
Similar Triangles
Similar Triangles Example 2
Collinear Then 180
Converse of the Supplementary Angles Theorem
Right Angle is 90 Degres
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Subtract Both Sides
Subtraction Example 2
Add Number to Both Sides
Add Number to Both Sides 2
Collinear Angles Property C
Similar Triangles Example 3
Similar Distances 2
Multiplication Property 2
Multiplicative Property of Equality Variation 1
Associative Property of Multiplication 2
Transitive Property Application 2
Substitution 10
Reordering Terms Theorem
Multiplicative Identity 3
Division Theorem
Substitution 11
Substitution 14
Multiplication Property 3
Reorder Terms
Reduction Property
Cross Multiply Theorem
Substitution 12
Substitution in Product
Distance Symmetry Example 5
Distance Symmetry Example 2
Equality Example
Distance Algebra Example
Distributive Property 4
Substitution Example 10
Collinear Points Property 2
Pythagorean Theorem
Pythagorean Theorem 2
Distance Symmetry Example 4
Substitution 6
Distance Symmetry Example 3
Pythagorean Theorem 3
Pythagorean Theorem 4

Proof: Similar Distances 2

Let's prove the following theorem:

if △ABC ∼ △XYZ, then (distance CB) / (distance ZY) = (distance BA) / (distance YX)

A B C X Y Z

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 △ABC ∼ △XYZ
Proof Table
# Claim Reason
1 (distance CB) / (distance ZY) = (distance CA) / (distance ZX) if △ABC ∼ △XYZ, then (distance CB) / (distance ZY) = (distance CA) / (distance ZX)
2 (distance CA) / (distance ZX) = (distance BA) / (distance YX) if △ABC ∼ △XYZ, then (distance CA) / (distance ZX) = (distance BA) / (distance YX)
3 (distance CB) / (distance ZY) = (distance BA) / (distance YX) if (distance CB) / (distance ZY) = (distance CA) / (distance ZX) and (distance CA) / (distance ZX) = (distance BA) / (distance YX), then (distance CB) / (distance ZY) = (distance BA) / (distance YX)
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