Similar Circles and Central and Inscribed Angles

Slides:



Advertisements
Similar presentations
Geometry Honors Section 9.1 Segments and Arcs of Circles
Advertisements

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.
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.
Lesson 5 Circles.
Tangents, Arcs, and Chords
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.
Circles.
10-6 CIRCLES AND ARCS Objective: To find the measures of central angles and arcs. To find the circumference and arc length.
Geometry Section 10.2 Arcs & Chords
Unit 6 Day 1 Circle Vocabulary. In your pairs look up the definitions for your vocabulary words.
Introduction In the third century B. C., Greek mathematician Euclid, often referred to as the “Father of Geometry,” created what is known as Euclidean.
Deriving the Formula for the Area of a Sector
Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.
Lesson 10.1a Circle Terminology.
Lesson 8-1: Circle Terminology
7.6: Circles and Arcs Objectives:
Lesson 8-1: Circle Terminology
Lesson 8-1: Circle Terminology
Circle Geometry.
11-3 Inscribed Angles Objective: To find the measure of an inscribed angle.
Geometry Honors Section 9.3 Arcs and Inscribed Angles
Introduction Circles have several special properties, conjectures, postulates, and theorems associated with them. This lesson focuses on the relationship.
10.1 – Tangents to Circles. A circle is a set of points in a plane at a given distance from a given point in the plane. The given point is a center. CENTER.
Lesson 8-1: Circle Terminology
1 Circles. 2 3 Definitions A circle is the set of all points in a plane that are the same distance from a fixed point called the center of the circle.
Circles Chapter 12.
Inscribed Angles Section 9-5. Inscribed Angles An angle whose vertex is on a circle and whose sides contain chords of the circle.
Inscribed Angles. Inscribed Angles and Central Angles A Central angle has a vertex that lies in the center of a circle. A n inscribed angle has a vertex.
Inscribed Angles Inscribed angles have a vertex on the circle and sides contain chords of the circle.
Section 9-5 Inscribed Angles. Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B C D are inscribed.
1 Lesson 2 Circles. 2 Arcs An arc is an unbroken part of a circle. For example, in the figure, the part of the circle shaded red is an arc. A semicircle.
11.1 Angles and Circles Learning Objective: To identify types of arcs and angles in a circle and to find the measures of arcs and angles. Warm-up (IN)
What’s a skey? Defining Circle Terms Use the examples and non-examples to write a good definition for each boldfaced term.
 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.
Chapter 7 Lesson 6 Objective: To find the measures of central angles and arcs and the circumference.
Warm up: 1.A _______________ is the set of all points equidistant from a given point called the _______________. 2.A _______________ is a segment that.
Essential UnderstandingEssential Understanding  You can find the length of part of a circle’s circumferences by relating it to an angle in the circle.
Chapter 10: Area 10.6 Circles & Arcs. Definitions circle: set of all points equidistant from a given point center: point that is equidistant from the.
Circles Vocabulary And Properties Vocabulary And Properties.
Learning About Circles Circle n An infinite set of coplanar points that are an equal distance from a given point. O M M.
Circles. Circle  Is the set of all points in a plane that are equal distance from the center. This circle is called Circle P. P.
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.
Geometry 7-6 Circles, Arcs, Circumference and Arc Length.
Copyright © Cengage Learning. All rights reserved. 12 Geometry.
Circles Presented by: Desiree Smith, Lauren Rudebush, Justin Dilmore.
Unit 4: CIRCLES Topic 11: C IRCLE M EASUREMENTS Topic 12: T HEOREMS A BOUT C IRCLE.
Entry Task Circles and Arcs What is a circle? Circle The set of all points in a plane that are the same distance from a given point (this point.
Chapter 7 Circles. Circle – the set of all points in a plane at a given distance from a given point in the plane. Named by the center. Radius – a segment.
Circles and Arcs. General Vocabulary: CIRCLE: the set of all points equidistant from a given point called the CENTER RADIUS: a segment that has one point.
10.6/10.7 Circles, Arcs, Segments, and Sectors
Tangent and Chord Properties
Circles Vocabulary.
Warm Up Make a list of activities you take part in each day. Give each activity a percentage value which represents the amount of time you spend doing.
Copyright © 2014 Pearson Education, Inc.
10.6: Circles and Arcs. 10.6: Circles and Arcs.
Circle Unit Notes AA1 CC.
Tangent and Chord Properties
Chord Central Angles Conjecture
Introduction In the third century b.c., Greek mathematician Euclid, often referred to as the “Father of Geometry,” created what is known as Euclidean geometry.
Unit 6 Day 1 Circle Vocabulary.
Module 19: Lesson 1 Central Angles & Inscribed Angles
CIRCLES OBJECTIVE: Learn the basic terminology for circles and lines and segments associated with circles.
Circles and Arcs Skill 46.
9-5 Inscribed Angles.
Y. Davis Geometry Notes Chapter 10.
Circles and Arcs.
10.6 Circles & Arcs.
Unit 6 Day 1 Circle Vocabulary.
Inscribed Angles.
Adapted from Walch Education
Presentation transcript:

Similar Circles and Central and Inscribed Angles Adapted from Walch Education

Pi, ( ), is the ratio of the circumference to the diameter of a circle, where the circumference is the distance around a circle the diameter is a segment with endpoints on the circle that passes through the center of the circle a circle is the set of all points that are equidistant from a reference point (the center) and form a 2-dimensional curve. A circle measures 360°. Concentric circles share the same center. Key Concepts 3.1.1: Similar Circles and Central and Inscribed Angles

Key Concepts, continued The diagram to the right shows circle A ( ) with diameter and radius The radius of a circle is a segment with endpoints on the circle and at the circle’s center; a radius is equal to half the diameter. Key Concepts, continued 3.1.1: Similar Circles and Central and Inscribed Angles

Key Concepts, continued All circles are similar and measure 360°. A portion of a circle’s circumference is called an arc. The measure of a semicircle, or an arc that is equal to half of a circle, is 180°. Arcs are named by their endpoints. Key Concepts, continued 3.1.1: Similar Circles and Central and Inscribed Angles

Semicircle The semicircle below can be named 3.1.1: Similar Circles and Central and Inscribed Angles

A part of the circle that is larger than a semicircle is called a major arc. It is common to identify a third point on the circle when naming major arcs. The major arc in the diagram to the right can be named Major Arc 3.1.1: Similar Circles and Central and Inscribed Angles

Minor Arc A minor arc is a part of a circle that is smaller than a semicircle. The minor arc in the diagram to the right can be named Minor Arc 3.1.1: Similar Circles and Central and Inscribed Angles

Key Concepts, continued Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure. The measure of an arc is determined by the central angle. A chord is a segment whose endpoints lie on the circumference of a circle. Key Concepts, continued 3.1.1: Similar Circles and Central and Inscribed Angles

Central Angle A central angle of a circle is an angle with its vertex at the center of the circle and sides that are created from two radii of the circle. Central angle Central Angle 3.1.1: Similar Circles and Central and Inscribed Angles

Inscribed Angle An inscribed angle of a circle is an angle formed by two chords whose vertex is on the circle. Inscribed Angle 3.1.1: Similar Circles and Central and Inscribed Angles

The Inscribed Angle Theorem An inscribed angle is half the measure of the central angle that intercepts the same arc. Conversely, the measure of the central angle is twice the measure of the inscribed angle that intercepts the same arc. The Inscribed Angle Theorem 3.1.1: Similar Circles and Central and Inscribed Angles

The Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc’s angle. The Inscribed Angle Theorem 3.1.1: Similar Circles and Central and Inscribed Angles

Corollaries to the Inscribed Angle Theorem Corollary 1 Two inscribed angles that intercept the same arc are congruent. Corollary 2 An angle inscribed in a semicircle is a right angle. Corollaries to the Inscribed Angle Theorem 3.1.1: Similar Circles and Central and Inscribed Angles

A car has a circular turning radius of 15. 5 feet A car has a circular turning radius of 15.5 feet. The distance between the two front tires is 5.4 feet. To the nearest foot, how much farther does a tire on the outer edge of the turning radius travel than a tire on the inner edge? Practice 3.1.1: Similar Circles and Central and Inscribed Angles

Step 1 Calculate the circumference of the outer tire’s turn. Formula for the circumference of a circle Substitute 15.5 for the radius (r). Simplify. Step 1 3.1.1: Similar Circles and Central and Inscribed Angles

Step 2 Calculate the circumference of the inside tire’s turn. First, calculate the radius of the inner tire’s turn. Since all tires are similar, the radius of the inner tire’s turn can be calculated by subtracting the distance between the two front wheels (the distance between each circle) from the radius of the outer tire’s turn. Step 2 3.1.1: Similar Circles and Central and Inscribed Angles

Step 2, continued Formula for the circumference of a circle Substitute 10.1 for the radius (r). Simplify. Step 2, continued 3.1.1: Similar Circles and Central and Inscribed Angles

Calculate the difference in the circumference of each tire’s turn. Find the difference in the circumference of each tire’s turn. The outer tire travels approximately 34 feet farther than the inner tire. Step 3 3.1.1: Similar Circles and Central and Inscribed Angles

Try it. Find the measures of ∠BAC and ∠BDC. 3.1.1: Similar Circles and Central and Inscribed Angles

Thanks for watching! ~ms. dambreville