question 15 of 25

true or false? if a parallelogram is inscribed in a circle, it must be a rectangle.

a. true
b. false

Question

question 15 of 25

true or false? if a parallelogram is inscribed in a circle, it must be a rectangle.

a. true
b. false

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", "Inscribed Quadrilateral Theorem", "Rectangle Definition" ], "new_concepts": [], "current_concepts": [ "Parallelogram Properties", "Inscribed Quadrilateral Theorem", "Rectangle Definition" ] } ## Analyze properties of inscribed quadrilaterals $$ \begin{aligned} &\angle A + \angle C = 180^\circ\ &\angle B + \angle D = 180^\circ \end{aligned} $$ ## Apply parallelogram properties $$ \begin{aligned} &\angle A = \angle C\ &\angle B = \angle D \end{aligned} $$ ## Solve for interior angles $$ \begin{aligned} &2\angle A = 180^\circ \implies \angle A = 90^\circ\ &2\angle B = 180^\circ \implies \angle B = 90^\circ\ &\angle A = \angle B = \angle C = \angle D = 90^\circ \end{aligned} $$

A. True

B. False

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Quadrilateral Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze properties of inscribed quadrilaterals

Apply parallelogram properties

Solve for interior angles

Answer: