10.3 Warmup Find the value of x given that C is the center of the circle and that the circle has a diameter of 12. November 24, 2018 Geometry 10.3 Using.

Slides:

Advertisements

Similar presentations

Warm Up. Properties of Chords  By the end of class today you will: Be able to identify congruent minor arcs in the same or congruent circles using chords.

Advertisements

In the diagram of C, QR = ST = 16. Find CU.

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.

Sect Properties of Chords and Arcs Geometry Honors.

Lesson 6.2 Properties of Chords

Unit 4: Arcs and Chords Keystone Geometry

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.

Apply Properties of Chords

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.

MM2G3 Students will understand properties of circles. MM2G3 d Justify measurements and relationships in circles using geometric and algebraic properties.

Chapter 10.3 Notes: Apply Properties of Chords

Geometry 9.4 Arcs and Chords.

10.3 – Apply Properties of Chords

11-2 Chords & Arcs 11-3 Inscribed Angles

GEOMETRY: Chapter : Chords#2. Image taken from: Geometry. McDougal Littell: Boston, P Theorem 10.4 In the same circle, or in congruent.

12.2 Chords and Arcs Theorem 12.4 and Its Converse Theorem –

Warm-Up a. mBD b. mACE c. mDEB d. mABC 140° 130° 230° 270°

MM2G3a Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

11-2 Chords and Arcs  Theorems: 11-4, 11-5, 11-6, 11-7, 11-8  Vocabulary: Chord.

9-3 Arcs and Chords Objectives: To recognize and use relationships among arcs, chords, and diameters.

10.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Properties of Chords.

Arcs and Chords Theorem 10.2 In a circle or in congruent circles, two minor arcs are are congruent if and only if their corresponding chords are congruent.

Geometry 9.4 Arcs and Chords. Theorem In the same circle or in congruent circles: congruent arcs have congruent chords congruent chords have congruent.

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.

Main Idea 1: If the arcs are congruent, then the chords are congruent. REVERSE: If the chords are congruent, then the arcs are congruent. Main Idea 2:

Circle Segments and Volume. Chords of Circles Theorem 1.

Circle Geometry.

10.3 Apply Properties of Chords Hubarth Geometry.

Goal 1: To use congruent chords, arcs, and central angles Goal 2: To recognize properties of lines through the center of a circle Check Skills You’ll Need.

10.2 Arcs and Chords Unit IIIC Day 3. Do Now How do we measure distance from a point to a line? The distance from a point to a line is the length of the.

Arcs and Chords Goal 1 Using Arcs of Circles

12.2 Chords and Arcs.

1. DC Tell whether the segment is best described as a radius,

Tell whether the segment is best described as a radius,

10.3 – Apply Properties of Chords

Unit 3: Circles & Spheres

Do Now 1.) Explain the difference between a chord and a secant.

Section 10.4 Arcs and Chords.

Chapter 10: Properties of Circles

Assignment 1: 10.3 WB Pg. 127 #1 – 14 all

Lesson 10-3 Arcs and Chords.

Lesson 8-4: Arcs and Chords

Geometry 11.4 Color Theory.

7-3 Arcs and Chords Objectives:

Chords, secants and tangents

1. DC Tell whether the segment is best described as a radius,

12-1 Tangent Lines.

Lesson 8-4: Arcs and Chords

Central angle Minor Arc Major Arc

Section 11 – 2 Chords & Arcs Objectives:

Lesson 8-4 Arcs and Chords.

Week 1 Warm Up Add theorem 2.1 here next year.

Central angle Minor Arc Major Arc

Section 10.2 Arcs and Chords.

EXAMPLE 1 Use congruent chords to find an arc measure

Arcs Chapter 9 Section-4 Chords.

Lesson 8-4: Arcs and Chords

Geometry Section 10.3.

Warm-up A E B D 37o C ( ( ( ( Find the measure of DC and AB and AD and ACD.

Standards: 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the.

12.2 Chords & Arcs.

Lesson 8-4: Arcs and Chords

Warm Up 1. Draw Circle O 2. Draw radius OR 3. Draw diameter DM

Chapter 9-4 Arcs and Chords.

Section 10.2 Arcs and Chords.

Presentation transcript:

10.3 Warmup Find the value of x given that C is the center of the circle and that the circle has a diameter of 12. November 24, 2018 Geometry 10.3 Using Chords

10.3 Warmup Factor Completely 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔 𝒙 𝟐 +𝟏𝟏𝒙+𝟐𝟒 4. 𝒙 𝟐 −𝟔𝒙+𝟗 5. 𝒙 𝟐 −𝟒𝒙−𝟓 6. 𝒙 𝟐 −𝟗 November 24, 2018 Geometry 10.3 Using Chords

10.3 Warmup (Answers) Factor Completely 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔 𝒙 𝟐 +𝟏𝟏𝒙+𝟐𝟒 4. 𝒙 𝟐 −𝟔𝒙+𝟗 5. 𝒙 𝟐 −𝟒𝒙−𝟓 6. 𝒙 𝟐 −𝟗 5𝑥(𝑥−7 6(𝑥+1)(𝑥+1 𝑥+8)(𝑥+3 𝑥−3)(𝑥−3 𝑥−5)(𝑥+1 𝑥−3)(𝑥+3 November 24, 2018 Geometry 10.3 Using Chords

Geometry 10.3 Using Chords mbhaub@mpsaz.org

10.3 Essential Question In a circle, what is true when a radius is perpendicular to a chord? November 24, 2018 Geometry 10.3 Using Chords

Goals Compute arc measures and angle measures November 24, 2018 Geometry 10.3 Using Chords

Arc Theorems November 24, 2018 Geometry 10.3 Using Chords

Congruent Corresponding Chords Theorem (Thm 10.6) In the same circle, or in congruent circles, two minor arcs are congruent if and only if corresponding chords are congruent. November 24, 2018 Geometry 10.3 Using Chords

Theorem 10.6 B A C D November 24, 2018 Geometry 10.3 Using Chords

Example 1 Solve for x. 5x + 10 = 120 5x = 110 x = 22 (5x + 10) 120 November 24, 2018 Geometry 10.3 Using Chords

Example 2 x 𝑥+𝑥+150=360 2𝑥+150=360 150 ͦ 2𝑥 =210 𝑥=105 x =105° November 24, 2018 Geometry 10.3 Using Chords

Perpendicular Chord Bisector Theorem (Thm 10.7) If a diameter is perpendicular to a chord, then it bisects the chord and the subtended arc. November 24, 2018 Geometry 10.3 Using Chords

Example 3 Solve for x. 2x = 52 x = 26 52 2x November 24, 2018 Geometry 10.3 Using Chords

Example 4 𝐶𝐸=5+5=10 9𝑥=80−𝑥 10𝑥=80 𝑥=8 =2∙9 8 =144° a. Find the length of 𝐶𝐸 . b. Find . 𝐶𝐸=5+5=10 9𝑥=80−𝑥 10𝑥=80 𝑥=8 =2∙9 8 =144° November 24, 2018 Geometry 10.3 Using Chords

Perpendicular Chord Bisector Converse Theorem (Thm 10.8) If a chord is the perpendicular bisector of another chord, then it is a diameter. Diameter November 24, 2018 Geometry 10.3 Using Chords

Equidistant Chords Theorem (Thm 10.9) Two chords are congruent if and only if they are equidistant from the center of a circle. November 24, 2018 Geometry 10.3 Using Chords

The red wires are the same length because they are the same distance from the center of the grate. November 24, 2018 Geometry 10.3 Using Chords

Example 5 Solve for x. 16 4x – 2 = 16 4x = 18 x = 18/4 x = 4.5 4x – 2 November 24, 2018 Geometry 10.3 Using Chords

Example 6 In the diagram, QR = ST = 16, CU = 2x, and CV = 5x − 9. Find the length of the radius of ⊙C. November 24, 2018 Geometry 10.3 Using Chords

Your Turn In the diagram, JK = LM = 24, NP = 3x, and NQ = 7x − 12. Find the radius of ⊙N. November 24, 2018 Geometry 10.3 Using Chords

Summary Congruent chords subtend congruent arcs and are equidistant from the center of the circle. If a diameter is perpendicular to a chord, then it bisects it. November 24, 2018 Geometry 10.3 Using Chords

Homework mbhaub@mpsaz.org November 24, 2018 Geometry 10.3 Using Chords