Download presentation

Presentation is loading. Please wait.

Published byLeslie Franklin Modified over 4 years ago

1
Bell work 1 T R TU = 92 º U Find the measure of the inscribed angles, R, given that their common intercepted TU = 92º

2
Bell work 1 Answer T R TU = 92 º U Angles R = ½ the intercepted arc TU since their intercepted Arc TU = 92º, then Angle R = 46º

3
Bell work 2 A quadrilateral WXYZ is inscribed in circle P, if _ X = 130º and _ Y = 106º, Find the measures of _ X = 130º and _ Y = 106º, Find the measures of _ W = ? and _ Z = ? _ W = ? and _ Z = ? X Y P Z The Quadrilateral WXYZ is inscribed in the circle iff / X + / Z = 180º, and / W + / Y = 180º W 130 º 106 º

4
Bellwork 2 Answer From Theorem 10.11 _ W = 180º – 106º = 74º and _ W = 180º – 106º = 74º and _ Z = 180º – 130º = 50º _ Z = 180º – 130º = 50º X Y P Z The Quadrilteral WXYZ is inscribed in the circle iff / X + / Z = 180º, and / W + / Y = 180º W 130 º 106 º

5
Unit 3 : Circles: 10.4 Other Angle Relationships in Circles Objectives: Students will: 1.Use angles formed by tangents and chords to solve problems related to circles 2.Use angles formed by lines intersecting on the interior or exterior of a circle to solve problems related to circles

6
(p. 621) Theorem 10.12 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is ½ the measure of its intercepted arc P A B Angle 1 C m _ 1 = ½ m minor AC m _ 2 = ½ m Major ABC Angle 2 m

7
(p. 621) Theorem 10.12 Example 1 Find the measure of Angle 1 and Angle 2, if the measure of the minor Arc AC is 130 º P A B Angle 1 C º m minor AC = 130º Angle 2 m

8
(p. 621) Theorem 10.12 Example 1 Answer The measure of Angle 1 = 65 º and Angle 2 = 115 º P A B 65 º = Angle 1 C º m minor AC = 130º Angle 2 = 115 º m

9
(p. 621) Theorem 10.12 Example 2 Find the measure of Angle 1, if Angle 1 = 6x º, and the measure of the minor Arc AC is (10x + 16) º P A B Angle 1= 6x º C º m minor AC = (10x + 16)º m

10
(p. 621) Theorem 10.12 Example 2 Answer Angle 1 = 6xº = ½ Arc AC = ½ (10x + 16)º 6xº = ½ (10x + 16)º 6xº = 5x + 8 x = 8º thus, Angle 1 = 48º P A B Angle 1= 6x º C º m minor AC = (10x + 16)º m

11
Intersections of lines with respect to a circle There are three places two lines can intersect with respect to a circle. On the circle In the circle Outside the cirlce

12
(p. 622) Theorem 10.13 If two chords intersect in the interior of a circle, then the measure of each angle is ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle. P D C Angle 1 B m _ 1 = ½ (m AB + m CD) m _ 2 = ½ (mBC + mAD) Angle 2 A

13
m CD = 16 º (p. 622) Theorem 10.13 Example Find the value of x. P D C Angle 1 B m AB = 40 º A xºxº

14
m CD = 16 º (p. 622) Theorem 10.13 Example Answer x = ½ (m AB + m CD) = ½ (40º + 16º) x = ½ (56º) x = 28 º P D C Angle 1 B m AB = 40 º A xºxº

15
3 2 1 (p. 622) Theorem 10.14 If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is ½ the difference of the intercepted arcs. B m _ 1 = ½ (m BC – m AC) m _ 2 = ½ (m PQR – m PR) 1 Tangent and 1 Secant 2 Tangents2 Secants B A C m _ 3 = ½ (m XY – m WZ) P Q R W X Y Z

16
xºxº (p. 622) Theorem 10.14 Example 1 Find the value of x m _ x = ½ (m PQR - mPR) Major Arc PQR = 266 º P Q R

17
xºxº (p. 622) Theorem 10.14 Example 1 Answer m PR = (360º - m PQR) = (360º - 266º) = 94º x = ½ (m PQR - m PR) = ½ (266º - 94º) = ½ (172º) x = 86 º m _ x = ½ (m PQR - mPR) Major Arc PQR = 266 º P Q R

18
(p. 622) Theorem 10.14 Example 2 Find the value of x, GF. The m EDG = 210 º The m angle EHG = 68 º m _ EHG = 68 º = ½ (m EDG – m GF) E H G xºxº F 68 º D Major Arc EDG = 210 º

19
(p. 622) Theorem 10.14 Example 2 Answer m _ EHG = 68º = ½ (m EDG – m GF) 68º = ½ ( 210º - xº ) 136º = 210º - xº xº = 210º - 136º xº = 74º m _ EHG = 68 º = ½ (m EDG – m GF) E H G xºxº F 68 º D Major Arc EDG = 210 º

20
Home work PWS 10.4 A P. 624 (8 -34) even

21
Journal Write two things about the intersections of chords, secants, and/or tangents related to circles from this lesson.

Similar presentations

OK

10.5 Inscribed Angles. An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords. Intercepted arc: the arc.

10.5 Inscribed Angles. An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords. Intercepted arc: the arc.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on wireless communication Ppt on object-oriented concepts tutorial Numeric display ppt on tv Ppt on bullet train in india Ppt on network security basics Ppt on tcp ip protocol chart Ppt on project management tools Ppt on supply chain mechanism 7 segment led display ppt online Ppt on motivational skills