3. determine whether a triangle can have the following sides with the given lengths. (lesson 7.3) (1 point)
a. 5 mi, 19 mi, 15 mi.
b. 4 ft, 3 ft, 10 ft.

4. write the angles of $\delta def$ in order from smallest to largest. (lesson 7.3) (0.5 points)

5. write the sides of $\delta ghi$ in order from smallest to largest. (lesson 7.3) (0.5 points)

Question

3. determine whether a triangle can have the following sides with the given lengths. (lesson 7.3) (1 point)
a. 5 mi, 19 mi, 15 mi.
b. 4 ft, 3 ft, 10 ft.

4. write the angles of $\delta def$ in order from smallest to largest. (lesson 7.3) (0.5 points)

5. write the sides of $\delta ghi$ in order from smallest to largest. (lesson 7.3) (0.5 points)

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem", "Side-Angle Relationship" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem", "Side-Angle Relationship" ] } ## Apply the Triangle Inequality Theorem to Question 3 $$ \begin{aligned} &\text{3a. } 5 + 15 = 20 > 19 \implies \text{Yes} \ &\text{3b. } 4 + 3 = 7 < 10 \implies \text{No} \end{aligned} $$ ## Order angles by opposite side lengths for Question 4 $$ \begin{aligned} &DE = 1\frac{1}{4} = 1.25,\quad FE = 2,\quad FD = 2\frac{1}{8} = 2.125 \ &DE < FE < FD \implies m\angle F < m\angle D < m\angle E \end{aligned} $$ ## Order sides by opposite angle measures for Question 5 $$ \begin{aligned} &m\angle I = 180^\circ - (59^\circ + 61^\circ) = 60^\circ \ &m\angle G < m\angle I < m\angle H \implies IH < GH < GI \end{aligned} $$ ## Question 3 a. Yes b. No ## Question 4 $\angle F, \angle D, \angle E$ ## Question 5 $IH, GH, GI$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the Triangle Inequality Theorem to Question 3

Order angles by opposite side lengths for Question 4

Order sides by opposite angle measures for Question 5

Answer:

Question 3

Question 4

Question 5