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What is a theorem?
A theorem is a statement that has been proven based on previously established statements, such as other theorems and generally accepted statements (axioms). It requires a logical proof.
What is an axiom?
An axiom is a statement accepted as true without proof, serving as a starting point for further reasoning and arguments. It is considered a self-evident truth.
What is a corollary?
A corollary is a statement that follows directly from a theorem or an axiom with little or no additional proof required. It is a consequence or a result that naturally emerges from the established statement.
What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse's length is equal to the sum of the squares of the other two sides. In formula form: a² + b² = c².
What is the Transitive Property Corollary?
The Transitive Property Corollary states that if a = b and b = c, then a = c. This property is frequently used in mathematical proofs to establish equality relationships.
What is the definition of the Angle at the Centre Theorem?
The Angle at the Centre Theorem states that an angle formed at the center of a circle by two radii is twice the angle formed at the circumference by the same arc. In other words, Angle at Centre = 2 × Angle at Circumference.
State the Tangent and Radius Theorem.
The Tangent and Radius Theorem states that a radius drawn to the point of tangency is perpendicular to the tangent line at that point.
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What is the Inscribed Angle Theorem?
The Inscribed Angle Theorem states that an angle inscribed in a semicircle is a right angle (90 degrees).
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Explain the Alternate Segment Theorem.
The Alternate Segment Theorem states that the angle formed between a tangent and a chord through the point of contact is equal to the angle formed in the alternate segment of the circle.
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What is the definition of the Circle Theorems regarding Chords and Tangents?
The Circle Theorems regarding chords and tangents state that when a chord and a tangent intersect at a point on the circle, the angle between the chord and the tangent is equal to the angle subtended by the chord in the alternate segment of the circle.
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