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Questions and Answers
What is a chord?
What is a chord?
What is a secant?
What is a secant?
A line that intersects a circle in two points.
What is a diameter?
What is a diameter?
A chord that passes through the center of the circle.
What is a tangent?
What is a tangent?
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State Theorem 10.1.
State Theorem 10.1.
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State Theorem 10.2.
State Theorem 10.2.
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State Theorem 10.3.
State Theorem 10.3.
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What is the Arc Addition Postulate (Postulate 26)?
What is the Arc Addition Postulate (Postulate 26)?
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State Theorem 10.4.
State Theorem 10.4.
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State Theorem 10.5.
State Theorem 10.5.
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State Theorem 10.6.
State Theorem 10.6.
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State Theorem 10.7.
State Theorem 10.7.
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State Theorem 10.8.
State Theorem 10.8.
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State Theorem 10.9.
State Theorem 10.9.
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State Theorem 10.10.
State Theorem 10.10.
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State Theorem 10.11.
State Theorem 10.11.
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State Theorem 10.12.
State Theorem 10.12.
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State Theorem 10.13.
State Theorem 10.13.
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State Theorem 10.15.
State Theorem 10.15.
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Study Notes
Circle Terminology
- Chord: A segment with endpoints on a circle.
- Secant: A line that intersects a circle at two distinct points.
- Diameter: A special chord that passes through the center of the circle.
- Tangent: A line that touches the circle at exactly one point.
Key Theorems
- Theorem 10.1: A tangent line is perpendicular to the radius at the point of tangency.
- Theorem 10.2: If a line is perpendicular to a radius at its endpoint, it is a tangent line.
- Theorem 10.3: Tangent segments drawn from the same exterior point to a circle are congruent.
- Theorem 10.4: In the same or congruent circles, two minor arcs are congruent if their corresponding chords are congruent.
- Theorem 10.5: A diameter that is perpendicular to a chord bisects both the chord and its arc.
- Theorem 10.6: If one chord is the perpendicular bisector of another, then the first chord must be a diameter.
- Theorem 10.7: Two chords are congruent if they are equidistant from the center of the circle.
Angles and Arcs
- Theorem 10.8: An inscribed angle measures half that of its intercepted arc.
- Theorem 10.9: Inscribed angles that intercept the same arc are congruent.
- Theorem 10.10: An inscribed right triangle has its hypotenuse as the diameter of the circle.
- Theorem 10.11: A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
Intersecting Chords and Angles
- Theorem 10.12: The angle formed by a tangent and a chord at the point of intersection is half the measure of the intercepted arc.
- Theorem 10.13: For two intersecting chords in a circle, each angle's measure is half the sum of the measures of the intercepted arcs and their vertical angles.
- Theorem 10.15: The product of the lengths of segments of one chord equals the product of the lengths of segments of another chord intersecting inside the circle.
Additional Theorems
- Theorem 10.14 and Theorem 10.16-10.17 are not defined in the provided text.
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Description
Test your knowledge of key concepts in geometry with these flashcards focused on Chapter 10. Learn important terms like chord, secant, diameter, and tangent, alongside relevant theorems. Perfect for review before an exam or as a study aid!
