select the correct answer from each drop-down menu.

given: $\angle 3 \cong \angle 4$

prove: $\angle 1 \cong \angle 2$

by the linear pair theorem, $\angle 2$ is supplementary to $\angle 3$, which means $m\angle 2 + m\angle 3 = 180^\circ$. it is given that $\angle 3 \cong \angle 4$, so by the definition of congruent angles, $m\angle 3 = m\angle 4$. using the substitution property of equality, substitute $m\angle 4$ for $m\angle 3$ to rewrite the previous equation as $m\angle 2 + m\angle 4 = 180^\circ$. thus $\angle 2$ is supplementary to $\angle 4$ by the definition of supplementary angles. by the linear pair theorem, $\angle 1$ is supplementary to $\angle 4$. since $\angle 2$ and $\angle 1$ are supplementary to $\angle 4$, then by the congruent supplements theorem, $\angle 1 \cong \angle 2$.

use the paragraph proof to complete the two-column proof.

what statement and reason belong in line 5?

statements
1. $\angle 2$ is supplementary to $\angle 3$
2. $m\angle 2 + m\angle 3 = 180^\circ$
3. $\angle 3 \cong \angle 4$
4. $m\angle 3 = m\angle 4$
5. the angle sum of 2 and 4 is 180 degrees
6. $m\angle 2$ is supplementary to $m\angle 4$
7. $m\angle 1$ is supplementary to $m\angle 4$
8. $\angle 1 \cong \angle 2$

reasons
1. linear pair theorem
2. definition of supplementary angles
3. given
4. definition of congruence
5. choose an answer
6. choose an answer
7.
8.

Question

select the correct answer from each drop-down menu.

given: $\angle 3 \cong \angle 4$

prove: $\angle 1 \cong \angle 2$

by the linear pair theorem, $\angle 2$ is supplementary to $\angle 3$, which means $m\angle 2 + m\angle 3 = 180^\circ$. it is given that $\angle 3 \cong \angle 4$, so by the definition of congruent angles, $m\angle 3 = m\angle 4$. using the substitution property of equality, substitute $m\angle 4$ for $m\angle 3$ to rewrite the previous equation as $m\angle 2 + m\angle 4 = 180^\circ$. thus $\angle 2$ is supplementary to $\angle 4$ by the definition of supplementary angles. by the linear pair theorem, $\angle 1$ is supplementary to $\angle 4$. since $\angle 2$ and $\angle 1$ are supplementary to $\angle 4$, then by the congruent supplements theorem, $\angle 1 \cong \angle 2$.

use the paragraph proof to complete the two-column proof.

what statement and reason belong in line 5?

statements
1. $\angle 2$ is supplementary to $\angle 3$
2. $m\angle 2 + m\angle 3 = 180^\circ$
3. $\angle 3 \cong \angle 4$
4. $m\angle 3 = m\angle 4$
5. the angle sum of 2 and 4 is 180 degrees
6. $m\angle 2$ is supplementary to $m\angle 4$
7. $m\angle 1$ is supplementary to $m\angle 4$
8. $\angle 1 \cong \angle 2$

reasons
1. linear pair theorem
2. definition of supplementary angles
3. given
4. definition of congruence
5. choose an answer
6. choose an answer
7.
8.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Column Proof" ], "new_concepts": [], "current_concepts": [ "Two-Column Proof", "Linear Pair Theorem", "Congruent Supplements Theorem" ] } ## Identify the statement in line 5 $$ \text{Statement 5: } m\angle2 + m\angle4 = 180^\circ $$ ## Analyze the transition from line 2 and line 4 to line 5 $$ \begin{aligned} &\text{Line 2: } m\angle2 + m\angle3 = 180^\circ \ &\text{Line 4: } m\angle3 = m\angle4 \ &\text{Line 5: } m\angle2 + m\angle4 = 180^\circ \end{aligned} $$ ## Determine the reason for line 5 $$ \text{Reason 5: substitution property of equality} $$ What statement and reason belong in line 5? - Statement 5: $m\angle2 + m\angle4 = 180^\circ$ - Reason 5: substitution property of equality { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Two-Column Proof" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the statement in line 5

Analyze the transition from line 2 and line 4 to line 5

Determine the reason for line 5

Answer: