4. find the measurement of $\overline{nl}$.
$nl = 2uv = 2(8) = 16$

6. solve for x.
$tv = 2ba$

Question

4. find the measurement of $\overline{nl}$.
$nl = 2uv = 2(8) = 16$

6. solve for x.
$tv = 2ba$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Midsegment Theorem", "Midsegment Properties", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "Triangle Midsegment Theorem", "Midsegment Properties", "Solving Linear Equations" ] } ## Identify the geometric relationship Using the *Triangle Midsegment Theorem* and *Midsegment Properties* knowledge points $$ \begin{aligned} &B \text{ is the midpoint of } TU \text{ and } A \text{ is the midpoint of } VU.\ &BA \text{ is a midsegment of } \triangle TUV.\ &TV = 2BA \end{aligned} $$ ## Set up the algebraic equation Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &TV = x + 14\ &BA = 11 + x\ &x + 14 = 2(11 + x) \end{aligned} $$ ## Solve the linear equation Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &x + 14 = 22 + 2x\ &14 = 22 + x\ &x = -8 \end{aligned} $$ $x = -8$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Midsegment Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship

Set up the algebraic equation

Solve the linear equation

Answer: