question 32 of 40

two right triangles that are not similar can still have a pair of congruent acute angles.

a. true

b. false

Question

question 32 of 40

two right triangles that are not similar can still have a pair of congruent acute angles.

a. true

b. false

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Similar Triangles", "Triangle Similarity Postulates" ], "new_concepts": [], "current_concepts": [ "Similar Triangles", "Triangle Similarity Postulates", "Acute Angle" ] } ## Analyze the similarity criteria for right triangles $$ \begin{aligned} &\text{Let } T_1 \text{ and } T_2 \text{ be two right triangles.}\ &\text{Each triangle has a } 90^\circ \text{ angle.}\ &\text{If they share a pair of congruent acute angles, then:}\ &\angle A_1 \cong \angle A_2 \quad (\text{acute angles})\ &\angle R_1 \cong \angle R_2 = 90^\circ \quad (\text{right angles}) \end{aligned} $$ ## Apply the Angle-Angle (AA) similarity postulate $$ \begin{aligned} &\text{By the AA Similarity Postulate, if two angles of one triangle are congruent to}\ &\text{two angles of another triangle, the triangles must be similar:}\ &T_1 \sim T_2 \end{aligned} $$ ## Evaluate the statement $$ \begin{aligned} &\text{The statement claims they "can still have a pair of congruent acute angles" while "not similar."}\ &\text{Since AA similarity guarantees they must be similar, this statement is false.} \end{aligned} $$

A. True

B. False

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the similarity criteria for right triangles

Apply the Angle-Angle (AA) similarity postulate

Evaluate the statement

Answer: