1 / 18

12.2 HW Solutions

12.2 HW Solutions. a) PL b) PM c) All radii of a circle are congruent d) Triangle LPN e) SAS f) CPCTC a) All radii of a circle are congruent b) AB ≅ CD c) Given d) SSS e) angle AEB ≅ CED f) Thm 12.1. 14 2 7 50 8 10 a) CE b) DE c) angle CEB d) angle DEA

herb
Download Presentation

12.2 HW Solutions

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. 12.2 HW Solutions a) PL b) PM c) All radii of a circle are congruent d) Triangle LPN e) SAS f) CPCTC a) All radii of a circle are congruent b) AB ≅ CD c) Given d) SSS e) angle AEB ≅ CED f) Thm 12.1 • 14 • 2 • 7 • 50 • 8 • 10 • a) CE b) DE c) angle CEB d) angle DEA • The Center of the circle • 6 • 5.4 • 8.9 • 12.5 • 9.9 • 20.8 • 108 • 90 • 123.9 or 124

  2. Inscribed Angles Section 12.3

  3. Three high-school soccer players practice kicking goals from the points shown in the diagram. All three points are along an arc of a circle. Player A says she is in the best position because the angle of her kicks towards the goal is wider than the angle of the other players’ kicks. Do you agree? Player B Player A Player C

  4. Vocabulary • Inscribed Angle • An angle whose vertex is on the circle and whose sides are chords of the circle • Intercepted Arc • The portion of the circle intercepted by an inscribed angle

  5. Theorem 12-9: Inscribed Angle Theorem • The measure of an inscribed angle is half the measure of its intercepted arc A B ? ° 45 ° 60° ?° C

  6. Three Cases for 12-9 Q R F 1) The center is on a side of the angle 2) The center is inside of the angle 3) The center is outside of the angle

  7. Circle O, with inscribed B and diameter BC mB = ½mAC Given: Prove: C A O B Statement Reason Given Definition of AC Tri. Ext. Ang. Thm. Isosceles Tri. Thm Substitution Division Prop. Of Equal. 1. BC is a diameter 2. mAC = mAOC 3. mAC = mA + mB 4. mA = mB 5. mAC =2mB 6. ½mAC = mB

  8. Find a and b P a˚ = 120° T 60˚ 30˚ Q S b˚ = 75° R

  9. Corollaries: Inscribed Angle Theorem • Two inscribed angles that intercept the same arc are congruent x 70˚

  10. Corollaries: Inscribed Angle Theorem 2) An angle inscribed in a semicircle is a right angle ( A semicircle is 180, ½ of that is 90) x° = 90°

  11. Corollaries: Inscribed Angle Theorem 3) The opposite angles of a quadrilateral inscribed in a circle are supplementary (opposite angles intercept the entire circle, ½ of 360 is 180) 70˚ x

  12. Corollaries: Inscribed Angle Theorem • Two inscribed angles that intercept the same arc are congruent • An angle inscribed in a semicircle is a right angle ( A semicircle is 180, ½ of that is 90) • The opposite angles of a quadrilateral inscribed in a circle are supplementary (opposite angles intercept the entire circle, ½ of 360 is 180)

  13. Find the measure of angles 1 and 2 40˚ 2 = 38° 70˚ 38˚ 70˚ 1 = 90°

  14. Theorem 12-10 • The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. B B D D O O C C GEOGEBRA

  15. Find x and y 110° J Q 90° 35˚ x˚ = 35° 70° y˚ = 55° L K

  16. Homework • Section: 12-3 • Pages: 681-683 • Questions: 4-22, 36, 38

  17. C P Circle O, with inscribed ∠ABC Given: Prove: O mABC = ½mAC A B 1. Circle O, inscribed ∠ABC 2. Draw diameter BP 3. mABP = ½AP 4. mCBP = ½PC 5. mABC = mABP + mABP 6. mABC = ½AP + ½PC 7. mABC = ½(AP+PC) 8. mABC = ½AC Given Def. of Diameter Thm. 12-9 Thm. 12-9 Ang. Add. Post. Substitution Distributing (factoring) Arc Addition Post.

  18. Post-Homework Review • CHAPTER REVIEW • Page: 707 • Questions: 6-14 • Section: 12-3 • Pages: 681-683 • Questions: 25

More Related