Flashcards on Thales’s theorem
Thales's Theorem: Understanding the Angle in a Semicircle
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Thales's Theorem
12 cards
Card 1
Question: What is Thales's Theorem about?
Answer: Thales's Theorem states that if A, B, and C are three distinct points on a circle, and the line segment AC is a diameter of that circle, then the angl
Card 2
Question: When did Thales of Miletus live, to whom Thales's Theorem is attributed?
Answer: Around the 6th century BCE.
Card 3
Question: What kind of angle is an angle inscribed in a semicircle, according to Thales's Theorem?
Answer: A right angle.
Card 4
Question: How is an inscribed angle defined?
Answer: An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle.
Card 5
Question: What forms a semicircle?
Answer: A diameter and the arc it subtends.
Card 6
Question: In the proof of Thales's Theorem, if O is the center of the circle and A, B, C are points on the circumference, what is the relationship between OA, O
Answer: OA = OB = OC, because they are all radii of the same circle.
Card 7
Question: What kind of triangles are ΔAOB and ΔBOC in the proof of Thales's Theorem, and why?
Answer: They are isosceles triangles because OA = OB and OB = OC (all are radii).
Card 8
Question: In an isosceles triangle, what is true about the angles opposite the equal sides?
Answer: The angles opposite the equal sides are equal.
Card 9
Question: If ∠OAB = α and ∠OCB = β in the proof of Thales's Theorem, what is ∠ABC equal to?
Answer: ∠ABC = α + β.
Card 10
Question: What is the sum of the interior angles of any triangle?
Answer: 180°.