1 / 28

Circles

Circles. Vocabulary And Properties. Circle. A set of all points in a plane at a given distance (radius) from a given point (center) in the plane. r. . center. Radius. A segment from a point on the circle to the center of the circle. r. . Congruent Circles.

benito
Download Presentation

Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Circles Vocabulary And Properties

  2. Circle A set of all points in a plane at a given distance (radius) from a given point (center) in the plane. r  center

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

  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 A segment whose endpoints lie on the circle. Segments AB & CD are chords of G B A  G D C

  7. Diameter A chord passing through the center of a circle. Segment IJ is a diameter of G J  G I

  8. Secant A line that passes through two points of the circle. A line that contains a chord.

  9. Tangent A line in the plane of the circle that intersects the circle in exactly one point. ●  ● The point of contact is called the Point of Tangency

  10. Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. C ● Three letters are required to name a semicircle: the endpoints and one point it passes through.  B A is a semicircle

  11. Minor Arc An arc of a circle that is smaller than a semicircle. C ● Two letters are required to name a minor arc: the endpoints. P  B PC or CB are minor arcs

  12. Major Arc An arc of a circle that is larger than a semicircle. C ●  B A ABC or CAB are major arcs

  13. Inscribed Angle An angle whose vertex lies on a circle and whose sides contain chords of a circle. A C B D <ABC & <BCD are inscribed angles

  14. Central Angle An angle whose vertex is the center of the circle and sides are radii of the circle. A B  K <AKB is a central angle

  15. Properties of Circles The measure of a central angle is two times the measure of the inscribed angle that intercepts the same arc. B A 2x P x C m<APB = 2 times m<ACB ½ m<APB = m<ACB

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

  17. Angles inscribed in the same arc are congruent. The m<AQB =m<APB both intercept arc AB. A B Q P m<QAP = m<PBQ Both angles intercept QP

  18. Every angle inscribed in a semicircle is an right angle.

  19. 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

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

  21. 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

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

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

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

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

  26. Area of a circle A=?

  27. Answer A=radius square times pi

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

More Related