4. prove that lines ab and cd are parallel.

statement | reason

5. given that ab || cd and \angle 1 = \angle 2, prove ac = ab.

Question

4. prove that lines ab and cd are parallel.

statement | reason

5. given that ab || cd and \angle 1 = \angle 2, prove ac = ab.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Straight Angle Theorem", "Consecutive Interior Angles Converse" ], "new_concepts": [ "Two-Column Proof" ], "current_concepts": [ "Straight Angle Theorem", "Consecutive Interior Angles Converse", "Two-Column Proof" ] } ## Identify the given geometric values Using the *Straight Angle Theorem* knowledge point $$ \begin{aligned} &\text{Let } E \text{ and } F \text{ be the intersection points on lines } AB \text{ and } CD \text{ respectively.}\ &m\angle AEF = 148^\circ\ &m\angle EFD = 32^\circ \end{aligned} $$ ## Calculate the consecutive interior angle sum Using the *Consecutive Interior Angles Converse* knowledge point $$ \begin{aligned} &m\angle AEF + m\angle EFD = 148^\circ + 32^\circ = 180^\circ \end{aligned} $$ ## Complete the two-column proof Using the *Consecutive Interior Angles Converse* knowledge point $$ \begin{array}{l|l} \textbf{Statement} & \textbf{Reason} \ \hline 1. \text{ Let } E \text{ and } F \text{ be points on } AB \text{ and } CD \text{ along transversal } EF. & 1. \text{ Given / Construction} \ 2. m\angle AEF = 148^\circ \text{ and } m\angle EFD = 32^\circ & 2. \text{ Given} \ 3. m\angle AEF + m\angle EFD = 180^\circ & 3. \text{ Addition Property of Equality} \ 4. AB \parallel CD & 4. \text{ Consecutive Interior Angles Converse} \end{array} $$ $$ \begin{array}{l|l} \textbf{Statement} & \textbf{Reason} \ \hline 1. m\angle AEF = 148^\circ \text{ and } m\angle EFD = 32^\circ & 1. \text{ Given} \ 2. m\angle AEF + m\angle EFD = 180^\circ & 2. \text{ Addition Property of Equality} \ 3. AB \parallel CD & 3. \text{ Consecutive Interior Angles Converse} \end{array} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Consecutive Interior Angles Converse" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric values

Calculate the consecutive interior angle sum

Complete the two-column proof

Answer: