question 39 of 40

is $\delta abc$ similar to $\delta def$? why or why not?

a. yes, because the angles are congruent and the sides are proportional.
b. we cannot tell because the third side is not given.
c. yes, because the angles are close enough and the sides are proportional.
d. no, because not all the angles are congruent.

Question

question 39 of 40

is $\delta abc$ similar to $\delta def$? why or why not?

a. yes, because the angles are congruent and the sides are proportional.
b. we cannot tell because the third side is not given.
c. yes, because the angles are close enough and the sides are proportional.
d. no, because not all the angles are congruent.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Similarity Postulates" ], "new_concepts": [], "current_concepts": [ "Triangle Similarity Postulates", "Triangle Angle Sum Theorem" ] } ## Compare corresponding angles of the two triangles $$ \begin{aligned} &m\angle A = 25^\circ,\quad m\angle D = 24^\circ \ &m\angle B = 95^\circ,\quad m\angle E = 96^\circ \ &m\angle C = 60^\circ,\quad m\angle F = 60^\circ \end{aligned} $$ ## Evaluate similarity criteria $$ \begin{aligned} &m\angle A eq m\angle D \ &m\angle B eq m\angle E \end{aligned} $$ Since corresponding angles are not congruent, the triangles are not similar.

A. Yes, because the angles are congruent and the sides are proportional.

B. We cannot tell because the third side is not given.

C. Yes, because the angles are close enough and the sides are proportional.

D. No, because not all the angles are congruent.

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

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Question

Explanation:

Compare corresponding angles of the two triangles

Evaluate similarity criteria

Answer: