consider the diagram.

which line segment has the same measure as $\overline{tq}$?

$\bigcirc$ $\overline{sr}$
$\bigcirc$ $\overline{tr}$
$\bigcirc$ $\overline{st}$
$\bigcirc$ $\overline{qs}$

Question

consider the diagram.

which line segment has the same measure as $\overline{tq}$?

$\bigcirc$ $\overline{sr}$
$\bigcirc$ $\overline{tr}$
$\bigcirc$ $\overline{st}$
$\bigcirc$ $\overline{qs}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Bisector Theorem" ], "new_concepts": [], "current_concepts": [ "Perpendicular Bisector Theorem", "Reflection Properties" ] } ## Identify the geometric properties of line $m$ relative to segment $\overline{QR}$ $$ \begin{aligned} &m \perp \overline{QR} \ &\text{Let } P \text{ be the intersection of line } m \text{ and } \overline{QR} \ &QP = PR \quad (\text{indicated by the tick marks on } \overline{QR}) \ &\text{Therefore, line } m \text{ is the perpendicular bisector of } \overline{QR} \end{aligned} $$ ## Apply the Perpendicular Bisector Theorem $$ \begin{aligned} &T \text{ lies on line } m \ &TQ = TR \end{aligned} $$ ## Match with the given options $$ \text{The segment with the same measure as } \overline{TQ} \text{ is } \overline{TR} $$

(A) $\overline{SR}$

(B) $\overline{TR}$

(C) $\overline{ST}$

(D) $\overline{QS}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Bisector Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of line \(m\) relative to segment \(\overline{QR}\)

Apply the Perpendicular Bisector Theorem

Match with the given options

Answer: