Chapter 10 Mr. Mills. Sum of Central Angles The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees.

Slides:

Advertisements

Similar presentations

Circles. Parts of a Circle Circle A circle is the set of all points in a plane that are a given distance from a given point in the plane, called the.

Advertisements

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Circle Theorems-“No Brainers”

Tangents, Arcs, and Chords

The given distance is called the radius

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

Chapter 11. If 2 sides of a triangle are radii then the triangle is ______________.

What do you mean? I Rule the World! Bulls eyeI’m on it! In-Mates and Ex-Cons S - words $ $ $ $ $ $ $ $

Circles Chapter 10.

12.2 Arcs and Chords.  Apply properties of Arcs  Apply properties of Chords.

1 Lesson 10.2 Arcs and Chords. 2 Theorem #1: In a circle, if two chords are congruent then their corresponding minor arcs are congruent. E A B C D Example:

Tangents to Circles (with Circle Review)

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.

Lesson 8-4: Arcs and Chords

Unit 4: Arcs and Chords Keystone Geometry

Chapter 4 Properties of Circles Part 1. Definition: the set of all points equidistant from a central point.

Geometry Arcs and Chords September 13, 2015 Goals  Identify arcs & chords in circles  Compute arc measures and angle measures.

10.2 Arcs and Chords Central angle Minor Arc Major Arc.

Sect Arcs and Chords Goal 1 Using Arcs of Circles Goal 2 Using chords of Circles.

Chapter 6: Properties of Circles

Inscribed Angles Find measures of inscribed angles Find measures of angles of inscribed polygons. Three congruent central angles are pictured. What is.

Arcs of a Circle. Arc: Consists of two points on a circle and all points needed to connect the points by a single path. The center of an arc is the center.

Circle Set of all points equidistant from a given point called the center. The man is the center of the circle created by the shark.

StatementReason 1. Given 2. Chords that intercept congruent arcs are congruent Example 1 3. All radii of a circle are congruent.

Arcs & Angles Chapter 10. Draw & Label Central Angle Minor Arc Major Arc k.

Chapter 10 Properties of Circles.

 A circle is defined by it’s center and all points equally distant from that center.  You name a circle according to it’s center point.  The radius.

Review May 16, Right Triangles The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the.

Circles Chapter 9. Tangent Lines (9-1) A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The.

6.3 – 6.4 Properties of Chords and Inscribed Angles.

Circles Chapter 12.

Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.

Circles, II Chords Arcs.

11-2 Chords & Arcs 11-3 Inscribed Angles

Geometry Chapter 9 Review. Secant A line that contains a chord of a circle. SECANT.P.P.

Lesson 8-1: Circle Terminology

Arcs and Chords Geometry.

Geometry/Trig 2Name: __________________________ Fill In Notes – 9.4 Chords and Arcs Date: ___________________________ Arcs can be formed by figures other.

A radius drawn to a tangent at the point of tangency is perpendicular to the tangent. l C T Line l is tangent to Circle C at point T. CT  l at T.

Chapter 10.2 Notes: Find Arc Measures Goal: You will use angle measures to find arc measures.

Circles Modified by Lisa Palen. Definitions Circle The CENTER of the circle is the point that is the same distance to every point on the circle. The distance.

Circles Chapter 10 Sections 10.1 –10.7.

GeometryGeometry Lesson 6.1 Chord Properties. Geometry Geometry Angles in a Circle In a plane, an angle whose vertex is the center of a circle is a central.

 A circle is defined by it’s center and all points equally distant from that center.  You name a circle according to it’s center point.  The radius.

Section 10-2 Arcs and Central Angles. Theorem 10-4 In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding.

PROPERTIES OF CIRCLES Chapter – Use Properties of Tangents Circle Set of all points in a plan that are equidistant from a given point called.

Geometry 7-6 Circles, Arcs, Circumference and Arc Length.

Objectives: To use the relationship between a radius and a tangent To use the relationship between two tangents from one point.

Unit 7 - Circles Parts of a Circle Radius: distance from the center to a point on the circle  2 circles are  if they have the same radius radius Chord:

Circles Chapter 10 Sections 10.1 –10.7.

Unit 3: Circles & Spheres

Tangent and Chord Properties

Lesson 10-3 Arcs and Chords.

Geometry 11.4 Color Theory.

Lesson 8-4: Arcs and Chords

8-5 Angles in Circles Welcome everyone!.

Tangent and Chord Properties

Tangent and Chord Properties

Central angle Minor Arc Major Arc

Lesson 8-4 Arcs and Chords.

Central angle Minor Arc Major Arc

Lesson 8-4: Arcs and Chords

Y. Davis Geometry Notes Chapter 10.

Copyright © Cengage Learning. All rights reserved.

Lesson 8-4: Arcs and Chords

Inscribed Angles.

Presentation transcript:

Chapter 10 Mr. Mills

Sum of Central Angles The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees. Draw circle p with radii PA, PB, PC. The sum of the measures of angles APB, BPC, CPA is 360 degrees.

Congruent Arcs In the same circle or congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent. Draw Circle P with radii PA and PB. Draw chord AB. Draw an angle CPD that is congruent to central angle APB.

Congruent arcs Draw circle E with congruent angles RED and SET. What do you know about Minor arcs RD and ST ? If arc ST has a length of 27 inches, what is the length of arc RD?

Congruent Minor Arcs In a circle or congruent circles, two minor arcs are congruent, if and only if their corresponding chords are congruent. Draw circle P with chord AB and Chord CD. So that the two chords are congruent.

Congruent Minor Arcs Draw circle E with congruent chords AB and CD. What do we know about arcs AB and CD? If the measure of arc AB is 56 degrees, what is the measure of arc CD?

Diameter or Radius In a circle, if a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. Draw circle P with chord AB and radius CP that is perpendicular to chord AB.

Diameter and Radius Draw circle E with radius EZ perpendicular to chord AB. Label the intersection of the chord and radius as point M. IF AB has length 10,Find AM and BM If AB has length 10 and the radius is 6 find EM, the distance form the center.

You do the Math P X M R RM = 8 XP = 3 Find MP

You do the Math P X M R RX = 12 XP = 5 Find MP Find XM Find RM

X M R ST You do the Math P If RM is congruent to ST, XP is 8, and XM is 6. Find PS Find ST Find Pl L

Page 543 #7 Tell why the measure of angle CAM is 28 degrees. Hint: Think SSS.

Page 543 # 8 Explain how to show that the measure of arc ES is 100 degrees. Hint: The sum of interior angles of a triangle is 180 degrees.

Page 543 # 9 Explain how to show the length of SC is 21 units.

Inscribed Angles An inscribed angle is an angle that has its vertex on the circle and its sides contained in chords of the circle.

Inscribed angles Intercepted Arc

Inscribed Angles Theorem If an angle is an inscribed angle, then the measure is equal to ½ the measure of the intercepted arc or(the measure of the intercepted arc is twice the measure of the inscribed angle. Inscribed angles