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

perpendicular bisector of $\overline{bc}$
angle bisector of $\angle a$
median of $\delta abc$
altitude of $\delta abc$
none of the above

Question

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

perpendicular bisector of $\overline{bc}$
  angle bisector of $\angle a$
  median of $\delta abc$
  altitude of $\delta abc$
  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": [ "Triangle Segments" ], "new_concepts": [], "current_concepts": [ "Triangle Segments", "Median of a Triangle" ] } ## Identify the properties of segment AD $$ \begin{aligned} &D \text{ is the midpoint of } \overline{BC} \text{ because } BD = DC \text{ (indicated by matching tick marks on } \overline{BD} \text{ and } \overline{DC}\text{).} \ &\overline{AD} \text{ connects vertex } A \text{ to the midpoint } D \text{ of the opposite side } \overline{BC}\text{.} \end{aligned} $$ ## Match with geometric definitions $$ \begin{aligned} &\text{Median of } \triangle ABC: \text{A segment from a vertex to the midpoint of the opposite side. (Matches } \overline{AD}\text{)} \ &\text{Perpendicular bisector of } \overline{BC}: \text{Requires } \overline{AD} \perp \overline{BC}\text{, which is not indicated.} \ &\text{Angle bisector of } \angle A: \text{Requires } \angle BAD \cong \angle CAD\text{, which is not indicated.} \ &\text{Altitude of } \triangle ABC: \text{Requires } \overline{AD} \perp \overline{BC}\text{, which is not indicated.} \end{aligned} $$ ## Select the correct option $$ \text{Correct Option: Median of } \triangle ABC $$

Perpendicular bisector of $\overline{BC}$

Angle bisector of $\angle A$

Median of $\triangle ABC$

Altitude of $\triangle ABC$

None of the above

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

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QUESTION IMAGE

Question

Explanation:

Identify the properties of segment AD

Match with geometric definitions

Select the correct option

Answer: