Question

sortable list

question 14

drag the reasons into the correct order to complete the 2-column proof.

given: \\(2m \angle abc = m \angle abd\\)

prove: \\(m \angle abc = m \angle cbd\\)

\

$$\begin{array}{|l|c|} \\hline \\text{statement} & \\text{reason} \\\\ \\hline 2m \\angle abc = m \\angle abd & (1) \\\\ \\hline m \\angle abd = m \\angle abc + m \\angle cbd & (2) \\\\ \\hline 2m \\angle abc = m \\angle abc + m \\angle cbd & (3) \\\\ \\hline m \\angle abc = m \\angle cbd & (4) \\\\ \\hline \\end{array}$$

start order

• angle addition postulate
• subtraction property of equality
• transitive property of equality
• given

Explanation:

Identify the given statement and reason

Using the Linear Equations knowledge point

$$ \text{Statement (1): } 2m\angle ABC = m\angle ABD \implies \text{Reason (1): Given} $$

Apply the Angle Addition Postulate

The diagram shows ray \(BC\) is in the interior of \(\angle ABD\).

$$ m\angle ABD = m\angle ABC + m\angle CBD \implies \text{Reason (2): Angle Addition Postulate} $$

Substitute the expressions

We substitute the expression for \(m\angle ABD\) from Statement (2) into Statement (1).

$$ 2m\angle ABC = m\angle ABC + m\angle CBD \implies \text{Reason (3): Substitution Property of Equality (or Transitive Property of Equality)} $$

Since "Substitution Property of Equality" is not in the list, but "Transitive Property of Equality" is provided:

$$ \text{Reason (3): Transitive Property of Equality} $$

Solve for the final relation

Subtract \(m\angle ABC\) from both sides of the equation in Statement (3).

$$ m\angle ABC = m\angle CBD \implies \text{Reason (4): Subtraction Property of Equality} $$

Answer:

No.	Statement	Reason
(2)	\(m\angle ABD = m\angle ABC + m\angle CBD\)	Angle Addition Postulate
(3)	\(2m\angle ABC = m\angle ABC + m\angle CBD\)	Transitive Property of Equality
(4)	\(m\angle ABC = m\angle CBD\)	Subtraction Property of Equality