Question

what geometric reason justifies the transition from statement 5 to statement 6? subtraction property of equality division property of equality transitive property substitution

Explanation:

To determine the geometric reason for the transition from statement 5 to 6, we analyze each option:

• Subtraction Property of Equality: Applies when subtracting the same quantity from both sides of an equation, not typically for geometric statement transitions here.
• Division Property of Equality: Applies when dividing both sides of an equation by the same non - zero quantity, not relevant for most geometric statement justifications in this context.
• Transitive Property: States that if \(a = b\) and \(b = c\), then \(a = c\). This is commonly used in geometric proofs to link equalities (e.g., equal angles, equal segments) derived from different statements.
• Substitution: Involves replacing a quantity with its equal, but it is more about replacing a single term, while transitive property links two equalities.

In geometric proofs, when moving from one statement (e.g., \(AB = CD\)) to another (e.g., \(CD = EF\)) to conclude \(AB = EF\), the Transitive Property is used. Assuming the transition from statement 5 to 6 follows this logical linking of equalities, the Transitive Property is the justifying reason.

Answer:

Transitive Property