order the side lengths $ij$, $jk$, and $ki$ from least to greatest.

(note that the figure is not drawn to scale.)

Question

order the side lengths $ij$, $jk$, and $ki$ from least to greatest.

(note that the figure is not drawn to scale.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorems" ], "new_concepts": [ "Angle-Side Relationships" ], "current_concepts": [ "Triangle Inequality Theorems", "Angle-Side Relationships", "Triangle Angle Sum Theorem" ] } ## Find the third angle of the triangle Using the *Triangle Inequality Theorems* knowledge point $$ \begin{aligned} m\angle I &= 180^\circ - (m\angle J + m\angle K) \ m\angle I &= 180^\circ - (50^\circ + 88^\circ) = 42^\circ \end{aligned} $$ ## Order the angles from least to greatest Using the *Triangle Inequality Theorems* knowledge point $$ \begin{aligned} 42^\circ &< 50^\circ < 88^\circ \ m\angle I &< m\angle J < m\angle K \end{aligned} $$ ## Order the opposite sides from least to greatest Using the *Triangle Inequality Theorems* knowledge point $$ \begin{aligned} JK &< KI < IJ \end{aligned} $$ Order the side lengths $IJ$, $JK$, and $KI$ from least to greatest: $JK < KI < IJ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorems" ] }

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QUESTION IMAGE

Question

Explanation:

Find the third angle of the triangle

Order the angles from least to greatest

Order the opposite sides from least to greatest

Answer: