to make sure that a given parallelogram is a rectangle, at least how many of its angles must measure 90°?

a. three
b. one
c. four
d. two

Question

to make sure that a given parallelogram is a rectangle, at least how many of its angles must measure 90°?

a. three
b. one
c. four
d. two

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallelogram Properties", "Rhombus and Rectangle Relationship" ], "new_concepts": [ "Rectangle Definition" ], "current_concepts": [ "Parallelogram Properties", "Rhombus and Rectangle Relationship", "Rectangle Definition" ] } ## Analyze properties of a parallelogram with one right angle $$ \begin{aligned} &\text{Let } ABCD \text{ be a parallelogram with } \angle A = 90^\circ.\ &\angle C = \angle A = 90^\circ \quad (\text{Opposite angles are equal})\ &\angle B = 180^\circ - \angle A = 90^\circ \quad (\text{Consecutive interior angles are supplementary})\ &\angle D = \angle B = 90^\circ \quad (\text{Opposite angles are equal}) \end{aligned} $$ ## Determine the minimum number of right angles required $$ \begin{aligned} &\text{If at least } 1 \text{ angle is } 90^\circ, \text{ then all } 4 \text{ angles must be } 90^\circ.\ &\text{Minimum required } = 1 \end{aligned} $$

(A) Three

(B) One

(C) Four

(D) Two

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Rectangle Definition" ] }

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Question

Explanation:

Analyze properties of a parallelogram with one right angle

Determine the minimum number of right angles required

Answer: