shown with the measures of the minor arcs. which segments are congruent?

$\overline{eh}$ and $\overline{ef}$
$\overline{gh}$ and $\overline{fe}$
$\overline{fg}$ and $\overline{eh}$
$\overline{ef}$ and $\overline{gf}$

Question

shown with the measures of the minor arcs. which segments are congruent?

$\overline{eh}$ and $\overline{ef}$
$\overline{gh}$ and $\overline{fe}$
$\overline{fg}$ and $\overline{eh}$
$\overline{ef}$ and $\overline{gf}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Congruent Chords Theorem" ], "new_concepts": [], "current_concepts": [ "Congruent Chords Theorem", "Arc Measure" ] } ## Identify the given arc measures $$ \begin{aligned} &m\widehat{EH} = 115^\circ \ &m\widehat{GF} = 115^\circ \end{aligned} $$ ## Apply the Congruent Chords Theorem $$ \begin{aligned} &m\widehat{EH} = m\widehat{GF} \implies \overline{EH} \cong \overline{GF} \end{aligned} $$ ## Match with the given options $$ \text{The segments } \overline{FG} \text{ (or } \overline{GF}\text{) and } \overline{EH} \text{ are congruent.} $$

$\overline{EH}$ and $\overline{EF}$

$\overline{GH}$ and $\overline{FE}$

$\overline{FG}$ and $\overline{EH}$

$\overline{EF}$ and $\overline{GF}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Congruent Chords Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures

Apply the Congruent Chords Theorem

Match with the given options

Answer: