Chapter 6: Properties of Circles

Slides:

Advertisements

Similar presentations

Tangents, Arcs, and Chords

Advertisements

The given distance is called the radius

CIRCLES 2 Moody Mathematics.

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 12.1 Common Core – G.C.2 Identify and describe relationships among inscribed angels, radii, and chords…the radius of a circle is perpendicular.

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

Circles Chapter 10.

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

Bell work Find the value of radius, x, if the diameter of a circle is 25 ft. 25 ft x.

JRLeon Geometry Chapter 6.1 – 6.2 HGHS

Unit 6 Day 1 Circle Vocabulary. In your pairs look up the definitions for your vocabulary words.

Tangents to Circles (with Circle Review)

Circles and Chords. Vocabulary A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.

Lesson 6.2 Properties of Chords

TODAY IN GEOMETRY…  Warm Up: Major and Minor Arcs  Learning Target : 10.3 You will use relationships of arcs and chords in a circle.  Independent practice.

Essential Question: How do I construct inscribed circles, circumscribed circles Standard: MCC9-12.G.C.3 & 4.

Bell work What is a circle?. Bell work Answer A circle is a set of all points in a plane that are equidistant from a given point, called the center of.

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.

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.

LESSON B: CIRCLE PROPERTIES Objectives: To determine and apply properties of chords, arcs, and central angles in circles. 10/10/2015Geometry/Mrs. McConaughy1.

6.3 – 6.4 Properties of Chords and Inscribed Angles.

Circles Chapter 12.

Circle Properties - Ch 6 Chord Central Angles Conjecture If two chords in a circle are congruent, then they determine two central angles that are…....congruent.

Circle Proofs Allie Buksha Geometry Mr. Chester.

Section 10.1 Theorem 74- If a radius is perpendicular to a chord, then it bisects the chord Theorem 74- If a radius is perpendicular to a chord, then it.

11-2 Chords & Arcs 11-3 Inscribed Angles

11.3: INSCRIBED ANGLES Objectives: Students will be able to… Apply the relationship between an inscribed angle and the arc it intercepts Find the measures.

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.

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)

12.2 Chords and Arcs Theorem 12.4 and Its Converse Theorem –

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.

10.3 Chords. Review Draw the following on your desk. 1)Chord AB 2)Diameter CD 3)Radius EF 4)Tangent GH 5)Secant XY.

Chord and Tangent Properties. Chord Properties C1: Congruent chords in a circle determine congruent central angles. ●

Circles Vocabulary And Properties Vocabulary And Properties.

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.

circle - set of all points in a plane at a given distance from a given point in the plane.

Section 10.2 – Arcs and Chords

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.

Chapter 10 Circles – 5 10 – 6.

 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.

circle - set of all points in a plane at a given distance from a given point in the plane.

Warm up ♥This will be graded in 10 minutes ° ° ° °

Objectives: To use the relationship between a radius and a tangent To use the relationship between two tangents from one 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 Chapter 10 Sections 10.1 –10.7.

12.2 Chords and Arcs.

Tangent and Chord Properties

Circles Vocabulary.

Chords and Arcs Geometry 11-2.

Chapter 10: Properties of Circles

Geometry 11.4 Color Theory.

Unit 4: Circles and Volume

Chords, secants and tangents

12.1 Tangent lines -Theroem 12.1: if a line is tangent to a circle, then it will be perpendicular to the radius at the point of tangency -Theroem 12.3:

Tangent and Chord Properties

Tangent and Chord Properties

Section 11 – 2 Chords & Arcs Objectives:

12.3 Inscribed Angles.

12.2 Chords & Arcs.

Lesson 8-4: Arcs and Chords

Inscribed Angles.

Presentation transcript:

Chapter 6: Properties of Circles Objective: Learn relationships among chords, arcs, and angles Discover properties of tangent lines Learn how to calculate the length of an arc

Match the terms to the examples Circle terms we know: Match the terms to the examples Terms 1. Congruent Circles 2. Concentric Circles 3. Radius 4. Chord 5. Diameter E. 6. Tangent 7. Minor Arc G. RQ H. PRQ I. PQR F. 8. Major Arc 9. Semicircle

Objective: Discover properties of chords Chord Properties Objective: Discover properties of chords

Central Angle PQR, PQS, RST, QST, and QSR are not central angles of circle P. AOB, BOC, COD, DOA, and DOB are central angles of circle O. A central angle has it vertex at the center of the circle

Inscribed Angle ABC, BCD, and CDE are inscribed angles. PQR, STU, and VWX are not inscribed angles. An inscribed angle has its vertex on the circle and its sides are chords.

Chord Central Angles Conjecture B A Construct large circle O Construct to congruent chords and label AB and CD Measure and compare angles the central angles of arcs AB & CD D C O Chord Central Angles Conjecture If two chords in a circle are congruent, then they determine two central angles that are ____________. congruent Chord Arcs Conjecture If two chords in a circle are congruent, then their intercepted arcs are congruent.

Pg 310 #1-12, 16, 19-22 Perpendicular bisector of a Chord Conjecture Construct the perpendicular for O to AB and O to CD. Label intersection M and N. Measure AM, BM, CN, DN Measure ON and OM D M N O B C Perpendicular bisector of a Chord Conjecture The perpendicular bisector of a chord passes through the _______ of the circle. Perpendicular to a Chord Conjecture The perpendicular from the center of a circle to a chord is the ___________ of the chord. Chord distance to Center Conjecture Two congruent chords in a circle are ___________ from the center of the circle. equidistant center bisector Pg 310 #1-12, 16, 19-22

Perpendicular to a Chord Conjecture The perpendicular from the center of a circle to a chord is the ___________ of the chord. bisector Chord distance to Center Conjecture Two congruent chords in a circle are ___________ from the center of the circle. equidistant Perpendicular bisector of a Chord Conjecture The perpendicular bisector of a chord passes through the _______ of the circle. center