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Understanding Circles: Vocabulary and Properties in Geometry

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Dive into the fascinating world of circles with this comprehensive overview of essential terms and properties you need to know. Discover definitions, such as radius, diameter, and chord, alongside key concepts like congruent circles, concentric circles, and the unique characteristics of minor and major arcs. Learn about inscribed and central angles, their relationships, and important properties, including the angles inscribed in a semicircle being right angles. Master the formulas for circumference and area to enhance your geometric skills!

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Understanding Circles: Vocabulary and Properties in Geometry

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  1. Core-Plus Mathematics Project Home Math Department Home SAHS Home Circles Vocabulary And Properties

  2. Circle A set of all points in a plane at a given distance from a given point in the plane. .

  3. Radius A segment from a point on the circle to the center of the circle.

  4. Congruent Circles Two circles whose radii have the same measure. R=3 cm R=3 cm

  5. Concentric Circles Two or more circles that share the same center. .

  6. Chord Is a segment whose endpoints lie on the circle. B A D C

  7. Diameter A chord passing through the center of a circle. J I

  8. Secant A line that contains a chord.

  9. Tangent A line in the plane of the circle that intersects the circle in exactly one point.

  10. Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. Is a semicircle

  11. Minor Arc An arc of a circle that is smaller than a semicircle. The minor arc is AP (clockwise) or PD (clockwise). P D A

  12. Major Arc An arc of a circle that is larger than a semicircle. The major arc would be PA (clockwise) or DP (counter clockwise). P A D

  13. Inscribed Angle An angle whose vertex lies on a circle and whose sides contain chords of a circle. A C B D

  14. Central Angle An angle whose vertex is the center of the circle. A B O

  15. Properties of Circles The measure of a central angle is two times the measure of the angle that subtends the same arc.

  16. If the m<C is 55, then the m<O is 110. Both angle C and angle O subtend the same arc, AB. Example B A O C

  17. Property #2 Angles inscribed in the same arc are congruent.

  18. The m<AQB and the m<APB are congruent because they both inscribe arc AB. The m<QAP and m<QBP would be congruent because they inscribe arc QP. Example A B Q P

  19. Property #3 Every angle inscribed in a semicircle is an right angle.

  20. Each of the three angles inscribed in the semicircle is a right angle. Example C D B Angle B, C, and D are all 90 degree angles. A E

  21. Property #4 The opposite angles of a quadrilateral inscribed in a circle are supplementary.

  22. Example The measure of angle D + angle B=180 The measure of angle C+angle A=180 B 65 A 70 110 C 115 D

  23. Property #5 Parallel lines intercept congruent arcs on a circle.

  24. Example Arc AB is congruent to Arc CD A B D C

  25. Formulas What are the two formulas for finding circumference? C= C=

  26. Answer C=2 pi r C=d pi

  27. Area of a circle A=?

  28. Answer A=radius square times pi

  29. The End Core-Plus Mathematics Project Home Math Department Home SAHS Home

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