your turn
1. find $dg$
2. find $rn$

Question

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Proportional Segments in Triangles", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "Proportional Segments in Triangles", "Solving Linear Equations", "Triangle Proportionality Theorem" ] } ## Set up proportion for Question 1 Using the *Proportional Segments in Triangles* knowledge point $$ \frac{EC}{CF} = \frac{ED}{DG} $$ ## Solve for DG in Question 1 Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} \frac{32}{24} &= \frac{40}{DG} \ \frac{4}{3} &= \frac{40}{DG} \ 4 \cdot DG &= 120 \ DG &= 30 \end{aligned} $$ ## Set up proportion for Question 2 Using the *Proportional Segments in Triangles* knowledge point $$ \begin{aligned} &MQ = 8,\quad QP = QS + SP = 3 + 1 = 4 \ &\frac{MQ}{QP} = \frac{MR}{RN} \end{aligned} $$ ## Solve for RN in Question 2 Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} \frac{8}{4} &= \frac{10}{RN} \ 2 &= \frac{10}{RN} \ RN &= 5 \end{aligned} $$ ## Question 1 $DG = 30$ ## Question 2 $RN = 5$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Proportionality Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up proportion for Question 1

Solve for DG in Question 1

Set up proportion for Question 2

Solve for RN in Question 2

Answer:

Question 1

Question 2