Lesson 9-3 Arcs and Central Angles (page 339)

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.
Tangents, Arcs, and Chords
1 9 – 3 Arcs and Central Angles. 2 Arcs and Central Angles A central angle of a circle is an angle with its vertex at the center of the circle. O Y Z.
Section 10 – 2 Find Arc Measures. Vocabulary Central Angle – An angle whose vertex is the center of the circle. Minor Arc – An arc whose measurement is.
Bell work Find the value of radius, x, if the diameter of a circle is 25 ft. 25 ft x.
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
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.
Arcs and Chords lesson 10.2a California State Standards 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles.
Section 9-3 Arcs and Central Angles. Central angle An angle with its vertex at the center of a circle. is a central angle Circle B.
Section 9-3 Arcs and central angles Central angle §An angle with its vertex at the center of the circle.
Section 9.5 INSCRIBED ANGLES. Inscribed Angle What does inscribe mean? An inscribed angle is an angle whose vertex is on a circle and whose sides contain.
6.3 – 6.4 Properties of Chords and Inscribed Angles.
Chapter Circle  A set of all points equidistant from the center.
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)
 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.
9.3 Arcs and Central Angles
Arc Lengths By the end of today, you will know about arcs and their measures and be able to do operations involving them.
Lesson 10.2 Arcs and Chords. Arcs of Circles Central Angle-angle whose vertex is the center of the circle. central angle.
November 19,  A central angle of a circle is an angle with its vertex at the center of the circle.  The figurebelow illustrates.
6.2 Find Arc Measures. Vocabulary A central angle of a circle is an angle whose vertex is the center of the circle. A semicircle is an arc with endpoints.
Chapter 10.2 Notes: Find Arc Measures Goal: You will use angle measures to find arc measures.
Answers to Homework CE: 1) a) 2 b) 2 c) 2 d) 2 e) 1 f) 0 2) a) 2 b) 1 c)-f) 0 3. a) B b) E Written Ex: 2) 2√34 4) 15 6) 12 8) a) 72 b) 18 c) 144.
Geometry Section 10-2 Find Arc Measures.
GeometryGeometry 10.2 Finding Arc Measures 2/24/2010.
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.
A circle can be named by its center using the  symbol. A circle with a center labeled C would be named  C. An unbroken part of a circle is called an.
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.
Unit 9 Standard 9a Arcs and Chords Learning Target: I can use properties of arcs and chords of a circle to find measurements.
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.
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?
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.
Arcs and Chords Goal 1 Using Arcs of Circles
Review Tangents, plus Arcs, Central Angles and Chords
Use isosceles and equilateral triangles
10-2 Angles and Arcs.
Copyright © 2014 Pearson Education, Inc.
Find Arc measures 10.2.
Lesson 9-3 Arcs and Central Angles (page 339)
Circle Basics.
Circles.
Warm – up Find the radius of the circle given the picture below.
Lesson 9-4 Arcs and Chords (page 344)
Arcs and Central Angles
Arcs and Central Angles
Obj: Use angle measures to find arc measures
8-5 Angles in Circles Welcome everyone!.
Arcs and Central Angles
Central angle Minor Arc Major Arc
straight and curved lines
10.2 Arc Measures.
Circles 3/30/09.
Central angle Minor Arc Major Arc
Arcs of a Circle.
Section 10.2 Arcs and Chords.
10.2 Vocabulary central angle semicircle arc adjacent arcs
Warmup  .
Chapter 9 Section 3 (Arcs and Central Angles) Central Angle:
Module 19: Lesson 1 Central Angles & Inscribed Angles
Bellringer Have Worksheet from Monday (plus p. 767 #6 – 8, 18 – 19 on back) and Notes out on your Desk Work on p. 779 #44 – 45.
Geometry Chapter : Find Arc Measures.
Circles and Arcs Skill 46.
Circles and Arcs.
Central Angles and Arc Measures
9-2 Angles and Arcs Objectives:
Measuring Angles and Arcs
Section 10.2 Arcs and Chords.
Presentation transcript:

Lesson 9-3 Arcs and Central Angles (page 339) Essential Question How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?

Arcs and Central Angles X B Q Y

CENTRAL ANGLE: an angle with its vertex at the center of a circle. ∠AQX , ∠AQB , ∠AQY , ∠XQB , ∠BQY , ∠XQY examples: A X B Q Y

ARC: an unbroken part of a circle . MINOR ARC examples: , , , , A X B Q Y

ARC: an unbroken part of a circle . MAJOR ARC examples: , , , , Middle letter gives the direction of the arc. A X B Q Y

SEMICIRCLES: if the endpoints of a minor arc are on a diameter . examples: and Middle letter gives the direction of the arc. You must use 3 letters! A Yes, there are two semi-circles! X B Q Y

MEASURE of a MINOR ARC: equals the measure of its central angle MEASURE of a MINOR ARC: equals the measure of its central angle. The measure of any minor arc is less than 180º . 90º A X B Q Y

MEASURE of a MAJOR ARC: equals 360º minus the measure of its minor arc MEASURE of a MAJOR ARC: equals 360º minus the measure of its minor arc. The measure of any major arc is between 180º and 360º . 90º 270º A X B Q Y

MEASURE of a SEMICIRCLE: equals 180º . X B Q Y

ADJACENT ARCS: (of a circle) are arcs with exactly one point in common. example: ________ = __________ Y X Z W

Postulate 16 Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.

In E, find the measure of the angle or the arc named. Example #1 In E, find the measure of the angle or the arc named. 80º A 70º E 1 B 80º D 80º 80º C

In E, find the measure of the angle or the arc named. Example #2 In E, find the measure of the angle or the arc named. m∠1 = ________ 70º A 70º 70º E 1 B 80º D 80º 80º C

In E, find the measure of the angle or the arc named. Example #3 In E, find the measure of the angle or the arc named. 150º 70º + 80º A 70º 70º E B 80º D 80º 80º C

In E, find the measure of the angle or the arc named. Example #4 In E, find the measure of the angle or the arc named. 290º 360º - 70º A 70º 70º E B 80º D 80º 80º C

CONGRUENT ARCS: arcs in the same circle or in CONGRUENT ARCS: arcs in the same circle or in congruent circles that have equal measures. example: ________ ≅ __________ A 70º 70º E B 80º D 80º 80º C

Theorem 9-3 In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent. A D 1 2 B C

If ∠1 ≅ ∠2, then ______ ≅ ______ A D 1 2 B C

Written Exercises on pages 341 & 342 Assignment Written Exercises on pages 341 & 342 1 to 8 and 16 to 20 ALL numbers See the example on page 340 for HELP on #’s17 to 20! How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?

#17 Milwaukee 43ºN 90º rcircle = ? 43ºN 6400km 0º rearth = 6400km

#17 Milwaukee 43ºN 90º rcircle = ? 43º 6400km 90º - 43º = 47º 43º 0º rearth = 6400km

Written Exercises on pages 341 & 342 Assignment Written Exercises on pages 341 & 342 RECOMMENDED: 1, 2, 3, 4, 5, 6, 8 REQUIRED: 7, 16, 17, 18, 19, 20 ~ BONUS: #23 ~ How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?

WORK leading to the final answer. ~ Bonus Assignment ~ #23 from page 343. Include diagram and WORK leading to the final answer. Worth 10 points. How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?