question 4 of 5
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 $m\angle 4$ in 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. choose an answer
6. choose an answer
7.
8.
reasons
1. linear pair theorem
2. definition of supplementary angles
3. given
4. definition of congruence
5. choose an answer
6. definition of supplementary angles
7. linear pair theorem
8. congruent supplements theorem
the angle sum of 3 and 4 is 180 degrees
angle 1 is supplementary to angle 3
the angle sum of 2 and 4 is 180 degrees
angle 3 is supplementary to angle 4

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Two-Column Proof", "Linear Pair Theorem", "Congruent Supplements Theorem" ], "current_concepts": [ "Two-Column Proof", "Linear Pair Theorem", "Congruent Supplements Theorem", "Angle Congruence" ] } ## Analyze the paragraph proof for line 5 The paragraph proof states: "Using the substitution property of equality, substitute $m\angle4$ in for $m\angle3$ to rewrite the previous equation as $m\angle2 + m\angle4 = 180^\circ$." ## Match with the two-column proof structure - Line 2: $m\angle2 + m\angle3 = 180^\circ$ (definition of supplementary angles) - Line 4: $m\angle3 = m\angle4$ (definition of congruence) - Line 5 Statement: Substituting $m\angle4$ for $m\angle3$ in line 2 yields $m\angle2 + m\angle4 = 180^\circ$, which translates to "the angle sum of 2 and 4 is 180 degrees". - Line 5 Reason: substitution property of equality (or substitution). ## Identify the correct dropdown options - Statement 5: "the angle sum of 2 and 4 is 180 degrees" - Reason 5: "substitution property of equality" (or "substitution") What statement and reason belong in line 5? - Statement 5: the angle sum of 2 and 4 is 180 degrees - Reason 5: substitution property of equality { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Two-Column Proof" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the paragraph proof for line 5

Match with the two-column proof structure

Identify the correct dropdown options

Answer: