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:

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<reasoning>

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).
\[
m\angle ABC = m\angle CBD \implies \text{Reason (4): Subtraction Property of Equality}
\]
</reasoning>

<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

</answer>

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Answer:

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<reasoning>

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).
\[
m\angle ABC = m\angle CBD \implies \text{Reason (4): Subtraction Property of Equality}
\]
</reasoning>

<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

</answer>

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