question 2 of 10

which descriptions from the list below accurately describe the relationship between $\triangle abc$ and $\triangle def$? check all that apply.

a. same size
b. congruent
c. similar
d. same shape

Question

question 2 of 10

which descriptions from the list below accurately describe the relationship between $\triangle abc$ and $\triangle def$? check all that apply.

a. same size
b. congruent
c. similar
d. same shape

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Similarity" ], "new_concepts": [], "current_concepts": [ "Triangle Similarity", "Triangle Congruence" ] } ## Compare corresponding angles Using the *Triangle Similarity* knowledge point $$ \begin{aligned} &\angle A = 22^\circ, \quad \angle B = 120^\circ, \quad \angle C = 38^\circ\ &\angle D = 22^\circ, \quad \angle E = 120^\circ, \quad \angle F = 38^\circ\ &\angle A = \angle D, \quad \angle B = \angle E, \quad \angle C = \angle F \end{aligned} $$ ## Compare corresponding side ratios Using the *Triangle Similarity* knowledge point $$ \begin{aligned} &\frac{DE}{AB} = \frac{10}{5} = 2\ &\frac{EF}{BC} = \frac{6}{3} = 2\ &\frac{DF}{AC} = \frac{14}{7} = 2\ &\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC} = 2 \end{aligned} $$ ## Determine geometric relationships Since the corresponding angles are equal and the corresponding sides are proportional with a scale factor of $2$: - The triangles have the **same shape** but different sizes. - Therefore, they are **similar**. - They are not congruent and do not have the same size.

A. Same size

B. Congruent

C. Similar

D. Same shape

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Similarity" ] }

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QUESTION IMAGE

Question

Explanation:

Compare corresponding angles

Compare corresponding side ratios

Determine geometric relationships

Answer: