(c) select all that describe $\overline{lm}$.

perpendicular bisector of $\overline{jk}$
angle bisector of $\angle l$
median of $\delta jkl$
altitude of $\delta jkl$
none of the above

Question

(c) select all that describe $\overline{lm}$.

perpendicular bisector of $\overline{jk}$
  angle bisector of $\angle l$
  median of $\delta jkl$
  altitude of $\delta jkl$
  none of the above

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Altitude of a Triangle", "Triangle Segments" ], "new_concepts": [], "current_concepts": [ "Altitude of a Triangle", "Triangle Segments", "Perpendicular Bisector", "Angle Bisector", "Median of a Triangle" ] } ## Analyze the geometric properties of segment LM $$ \begin{aligned} &\text{Segment } \overline{LM} \text{ connects vertex } L \text{ to the opposite side } \overline{JK}.\ &\overline{LM} \perp \overline{JK} \quad (\text{indicated by the right-angle mark at } M). \end{aligned} $$ ## Evaluate the definition of altitude $$ \begin{aligned} &\text{An altitude of a triangle is a segment from a vertex perpendicular to the opposite side.}\ &\text{Since } L \text{ is a vertex of } \Delta JKL \text{ and } \overline{LM} \perp \overline{JK}, \overline{LM} \text{ is an altitude of } \Delta JKL. \end{aligned} $$ ## Evaluate other options $$ \begin{aligned} &M \text{ is not marked as the midpoint of } \overline{JK} \implies \text{Not a perpendicular bisector or median.}\ &\overline{LM} \text{ is not shown bisecting } \angle L \implies \text{Not an angle bisector.} \end{aligned} $$

Perpendicular bisector of $\overline{JK}$

Angle bisector of $\angle L$

Median of $\Delta JKL$

Altitude of $\Delta JKL$

None of the above

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Altitude of a Triangle" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the geometric properties of segment LM

Evaluate the definition of altitude

Evaluate other options

Answer: