1 / 10

Arcs and Angles

Arcs and Angles. Class Investigation. Geometry 1/11/11. Get out HW, pencil, binder, and begin Do Now! Objectives: Describe and apply conjectures of inscribed angles. AGENDA Do Now! (5 min) Inscribed angles (25 min) Practice problems (20). Vocabulary.

noleta
Download Presentation

Arcs and Angles

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. Arcs and Angles Class Investigation

  2. Geometry 1/11/11 • Get out HW, pencil, binder, and begin Do Now! • Objectives: • Describe and apply conjectures of inscribed angles AGENDA • Do Now! (5 min) • Inscribed angles (25 min) • Practice problems (20)

  3. Vocabulary • Inscribed Angle: An angle created by 2 chords (<A) where the vertex lies on the circle • Semicircle: Half a circle • Secant: A line the intersects the circle at 2 points A Secant Line

  4. Inscribed angle review We know: Inscribed angle = ½ (arc) C A 60º B

  5. Inscribed angles • An angle inscribed in a semicircle is a right angle. C 90º A B

  6. Investigation 1 • Step 1: Pick two points on the edge of your circle and label them A and B • Step 2: Now pick a point that is not between A and B and label it point P • Step 3: Now draw the chords AP and BP and measure inscribed angle <APB • <APB = ____________ • Step 4: Now draw another point that is not between A and B and label it point Q • Step 5: Draw the chords AQ and BQ, and measure inscribed angle <AQP • <AQB = ____________ • Step 7: What do you notice about how <APB and <AQB compare?? A B P Q

  7. Inscribed Angles Intercepting Arcs Conjecture • Inscribed angles that intercept the same arc are congruent.

  8. Investigation 2 • Step 1: Now draw 4 points on the edge of your circle and label them A, B, C and D • Step 2: Now connect all four points with lines AB, BC, CD, and DA • Step 3: Now measure angles <A, <B, <C, and <D and add them all up • <A = _______ • <B = _______ • <C = _______ • <D = _______ D A C B

  9. Cyclic Quadrilateral Conjecture • A quadrilateral inscribed in a circle is called a cyclic quadrilateral • The opposite angles of a cyclic quadrilateral are supplementary.

  10. Parallel Lines Intercepted Arcs Conjecture • Parallel lines intercept congruent arcs on a circle. 43° 43°

More Related