given the following triangle, list the measure of the side lengths from smallest to largest.

$m\overline{bc}

Question

given the following triangle, list the measure of the side lengths from smallest to largest.

$m\overline{bc} < m\overline{ab} < m\overline{ac}$

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 Angle Sum Theorem", "Angle-Side Relationship" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Angle-Side Relationship" ] } ## Find the missing angle measure Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} m\angle A + m\angle B + m\angle C &= 180^\circ \ m\angle A + 65^\circ + 60^\circ &= 180^\circ \ m\angle A + 125^\circ &= 180^\circ \ m\angle A &= 55^\circ \end{aligned} $$ ## Order the angles from smallest to largest Using the *Angle Classification* knowledge point $$ 55^\circ < 60^\circ < 65^\circ $$ $$ m\angle A < m\angle C < m\angle B $$ ## Relate angle measures to opposite side lengths Using the *Angle-Side Relationship* knowledge point $$ \begin{aligned} \text{Opposite to } \angle A & ightarrow \overline{BC} \ \text{Opposite to } \angle C & ightarrow \overline{AB} \ \text{Opposite to } \angle B & ightarrow \overline{AC} \end{aligned} $$ $$ m\overline{BC} < m\overline{AB} < m\overline{AC} $$ Given the following triangle, list the measure of the side lengths from smallest to largest: $m\overline{BC} < m\overline{AB} < m\overline{AC}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angle-Side Relationship" ] }

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QUESTION IMAGE

Question

Explanation:

Find the missing angle measure

Order the angles from smallest to largest

Relate angle measures to opposite side lengths

Answer: