Lesson 9.5 Lines and Circles pp. 394-398.

Slides:



Advertisements
Similar presentations
Other Angle Relationships in Circles Section 10.4
Advertisements

Classifying Angles with Circles
Secants, Tangents, & Angle Measures Section 10-6.
Advanced Geometry Lesson 3 Circles
Angles Formed by Tangents, Chords, and Secants
Angles in a Circle Keystone Geometry
Other Angle Relationships
Session 25 Warm-up 1.Name a segment tangent to circle A. 2.What is the 3.If BD = 36, find BC. 4.If AC = 10 and BD = 24, find AB. 5.If AD = 7 and BD = 24,
Bellwork  One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle  Solve for x 2x.
Apply Other Angle Relationships in Circles
Geometry Section 10.4 Angles Formed by Secants and Tangents
Secants, Tangents and Angle Measures
Secants, Tangents, and Angle Measures
10.4: Angles formed by Secants and Tangents Obj: ______________________ __________________________.
10.1 Tangents to Circles Circle: the set of all points in a plane that are equidistant from a given point. Center: the point from which all points of.
10.4 Other Angles Relationships In Circles. Theorem A tangent and a chord intersect at a point, it makes angles that are ½ the intercepted arc.
Other Angle Relationships in Circles
Arcs and Angles Continued
Geometry – Inscribed and Other Angles
SECANTS Secant - A line that intersects the circle at two points.
Secants, Tangents and Angle Measures. Definition - Secant.
6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.
Inscribed Angles December 3, What is an inscribed angle? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords.
Section 10.5 Angles in Circles.
6.5 Other Angle Relationships in Circles. Theorem 6.13 If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed.
Geometry Warm-Up4/5/11 1)Find x.2) Determine whether QR is a tangent.
Lesson 9-6 Other Angles (page 357) Essential Question How can relationships in a circle allow you to solve problems involving angles of a circle?
Section 10.4 Other Angle Relationships in Circles.
Other Angle Relationships in Circles
Warm-Up A circle and an angle are drawn in the same plane. Find all possible ways in which the circle and angle intersect at two points.
Geometry Chapter 10 Section 6
Secants, Tangents, & Angle Measures
Module 19: Lesson 5 Angle Relationships in Circles
Secants, Tangents and Angle Measures
10.6 Secants, Tangents, and Angle Measures
Lesson 10-6: Secants and Tangents and Angle Measures
Section 10.5 Angles in Circles.
11.4 Angle Measures and Segment Lengths
4. What is the value of x in the following ?
Other Angle Relationships in Circles
Lesson 19.2 and 19.3.
Topic 12-4.
Do Now One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.
Module 19: Lesson 4 Segment Relationships in Circles
Chapter 10.5 Notes: Apply Other Angle Relationships in Circles
9-6 Other Angles.
Secant-Secant Angles Interior Secant Angle – An angle formed when two secants intersect inside a circle. Theorem A secant angle whose vertex is inside.
Section 6.2 More Angle Measures in a Circle
Lesson 8-5: Angle Formulas
Clock Activity 10.4 Please begin this activity
Angles Related to a Circle
Apply Other Angle Relationships
Secants, Tangents, and Angle Measure
Section 6.2 More Angle Measures in a Circle
Lesson 8-5: Angle Formulas
Lesson 9.4 Inscribed Angles pp
Unit 9 – Circles Acc. Alg/Geo A
Section 10.4 – Other Angle Relationships in Circles
Angles Related to a Circle
Lesson 8-5: Angle Formulas
Chapter 9 Section-6 Angles Other.
Lesson 8-5: Angle Formulas
Lesson 8-5: Angle Formulas
Lesson 8-5 Angle Formulas.
Secants, Tangents and Angle Measures
Lesson 8-5: Angle Formulas
Lesson 8-5: Angle Formulas
Secants, Tangents, and Angle Measures
Lesson 3-7: Secants and Tangents and Angle Measure
Lesson 8-5: Angle Formulas
Presentation transcript:

Lesson 9.5 Lines and Circles pp. 394-398

Objectives: 1. To find the measures of angles formed by intersecting lines based on the measures of the intercepted arcs. 2. To prove the relationships for such intersecting lines.

Theorem 9.17a The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.

If mCD = 100 and mBE = 30, then mBAE = O If mCD = 100 and mBE = 30, then mBAE = 35°

Theorem 9.18 The measure of an angle formed by two secants that intersect in the interior of a circle is one-half the sum of the measures of the intercepted arcs.

If mAB = 40 and mDC = 30, then m1 = Q 1 If mAB = 40 and mDC = 30, then m1 = 35°

Theorem 9.19 The measure of an angle formed by a tangent and a secant that intersect at the point of tangency is one-half the measure of the intercepted arc: mHIJ = ½mHI.

P H I J 1 If mHI = 120, then mHIJ = 60°

EXAMPLE Find the measure of ABC if BC is tangent to ⊙Q at B and AB is a secant. mAB = 170. Answer A Q B C 1 mABC = mAB 1 2 mABC = (170) 1 2 mABC = 85

Theorem 9.17b The measure of an angle formed by a secant and a tangent that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.

Theorem 9.17c The measure of an angle formed by the intersection of two tangents is one-half the difference of the measures of the intercepted arcs.

x 65º 111º x = 92º Theorem 9.18

x 64º 29º x = 122º Theorem 9.17a

x 23º 41º x = 9º Theorem 9.17a

58º x x = 244º Theorem 9.19

x 78º x = 102º Theorem 9.17c

67 x 128 x = 49º Theorem 9.17b

Homework pp. 396-398

►A. Exercises Find x. 9. x 86 36°

►A. Exercises Find x. 13. x 116°

18. Given: AC and BD are secants that 18. Given: AC and BD are secants that intersect inside circle E and form 1. Prove: m1 = ½(mAB + mDC) A D 1 B C E

■ Cumulative Review 24. Name the type of quadrilateral. Use the quadrilateral shown for the following questions. 24. Name the type of quadrilateral.

■ Cumulative Review 25. How do the diagonals relate? Use the quadrilateral shown for the following questions. 25. How do the diagonals relate?

■ Cumulative Review 26. perimeter. Use the quadrilateral shown for the following questions. If the diagonals of the quadrilateral shown are 10 and 6 inches respectively, give the 26. perimeter.

■ Cumulative Review 27. area. Use the quadrilateral shown for the following questions. If the diagonals of the quadrilateral shown are 10 and 6 inches respectively, give the 27. area.

■ Cumulative Review Use the quadrilateral shown for the following questions. 28. Name the type of polyhedron formed by using the quadrilateral shown as the base of a pyramid.