1 / 14

Lesson 45 – Angles and Arcs

Lesson 45 – Angles and Arcs. Homework Review. “Sheet 10 – Statements and Converses” ANY QUESTIONS???????????????. Problem of the Day. State the converse of the following. If you think the converse is true, rewrite the statement using iff . If you think it is false, give a counter example.

lucky
Download Presentation

Lesson 45 – Angles and Arcs

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. Lesson 45 – Angles and Arcs

  2. Homework Review • “Sheet 10 – Statements and Converses” • ANY QUESTIONS???????????????

  3. Problem of the Day • State the converse of the following. If you think the converse is true, rewrite the statement using iff. If you think it is false, give a counter example. • If a triangle has two congruent angles, then it is isosceles. • If a quadrilateral is a square, then it has four equal sides.

  4. Problem of the Day • Given chords XY, XZ and YZ are equidistant from the centre, C, of a circle, prove that the triangle XYZ is equilateral. • Given two circle with centre C (concentric circles) have chords AB and PQ respectively, CX is perpendicular to AB, and A-P-X-Q-B, prove that AP=BQ. • Given circles with centre A and B intersect at P and Q, and M is the midpoint of PQ, prove that A-M-B.

  5. Arcs, Angles and Chord Vocabulary

  6. C  B  A   D Arc – A Portion of a Circle’s Circumference • Minor Arc – An arc that is less than 180˚ • E.g. • Major Arc – An arc that is greater than 180˚ • E.g (specified using the endpoints and an internal point of the arc)

  7. C A B Central Angle – The Angle at the Centre of a Circle. • A central angle and a its intercepted arc are congruent. • They are both measured in degrees. • ACB is central angle subtended by arc AB • The measure of arc AB is equal to the measure of ACB • arcAB= ACB

  8. D C A B Inscribed Angle – The Angle Formed by Two Chords that Meet at the Same Point on a Circumference. • The measure of an inscribed angle is equal to half the measure of the arc intercepted by the inscribed angle. • The measure of an inscribed angle is equal to half the measure of a central angle subtended by the same arc. • E.g. If then AND arcAB=80˚

  9. D E F A B More Inscribed Angles: The Bow-Tie Rule • All inscribed angles subtended by same chord (AB) are equal. • E.g.

  10. C  Inscribed Angles and the Diameter • Inscribed angles subtended by the diameter measure 90˚. • The central angle would be 180˚ since the diameter is a straight line. • Inscribed angles are always equal to half of the central angle.

  11. X W Y Z Cyclic Quadrilateral – A Quadrilateral Inscribed in a Circle • Sum of the opposite angles of a cyclic quadrilateral are 180˚.

  12. C A B Sector – Part of the Interior of a Circle Bounded by Two Radii and the Arc Between them.

  13. minorsegment majorsegment Segment – Part of a Circle’s Interior Bounded by a Chord and Arc • Major segments are more than half of a circle’s area. • Minor segments are less than half of a circle’s area.

  14. You Try! • Complete “Sheet 11.1 [and] 11.2 – Angles and Arcs”

More Related