DO NOW #1. Please: Get a circle packet

Transcription

1 irclengles.gsp pril 26, 2013 Please: Get a circle packet Reminders: R #10 due Friday Quiz Monday 4/29 Quiz Friday 5/3 Quiz Wednesday 5/8 Quiz Friday 5/10 Initial Test Monday 5/13 ctual Test Wednesday 5/15 NW #1 1. raw circle with diameter 'd' with endpoints and on the circle. How many degrees is the arc from point to? 2. Now draw a line which is the perpendicular bisector of. Label points and where it intersects the circle. What is the measure of arc of and of? 3. How many degrees is the angle which creates those arcs? 1

2 pril 26, 2013 ircles Packet Name Period Intro to ircle- efinitions Name efinition iagram Notation 1. ircle (p. 566) Is a set of all points equidistant from a given point called the center. Mark and label the center. Name your circle. ircle 2. Radius (p. 566) Is a segment that has one endpoint at the center and the other endpoints on the circle. raw and label the radius Name your radius. (The segment with a bar over it.) 3. entral ngle (p. 566) Is an angle whose vertex is the center of the circle. raw 2 radii and label points and on the circle. Name your central angle. 4. Minor rc (p. 567) Is smaller than a semicircle. Highlight or bold the minor arc. Label your points. Name your arc. 5. Major rc (p. 567) Is greater than a semicircle. Highlight or bold the major arc. Label your points. Name your arc. 6. Semicircle (p. 567) Is half a circle Highlight or bold one semicircle. Label your Name your semicircle. points. 7. egree measure of an arc It is equal to the measure of the central angle that intercepts the arc. m 2

3 pril 26, 2013 entral ngles - Theorems Fact Theorem Postulate raw a picture to illustrate the fact. 1. ll radii of the same circle are congruent. 2. The measure of a semicircle is The measure of a major arc is 360 minus the measure of its related minor arc If and are 2 arcs with a common endpoint, (and not other points in common), then + = and m + m = m. This is the rc ddition Postulate 5. The measure of a central angle is equal to the measure of the intercepted arc. 65 Example I entral ngles In circle, GE is a straight angle, m GE = 180, and m FG = 80. The degree measure of FG is 80 o. (mfg = 80) Since mgfe = 180, 1. mfe 2. mfeg G 80 F 80 E is a diameter Example II Minor and Major rcs & rc ddition Postulate 1. Minor rc: + = 2. Major rc + = m = m + m m = m + m 40 o 90 o 3

4 pril 26, 2013 Example III entral ngles and rc ddition Postulate Let and be opposite rays and m = 75. Find 1. m 2. m 3. m = m m = m = m 75 o 4. m 5. m = m = m + m or m m nswers: entral ngles Examples Example I entral ngles In circle, GE is a straight angle, m GE = 180, and m FG = 80. The degree measure of FG is 80 o. (mfg = 80) Since mgfe = 180, 1. mfe 2. mfeg = = = 100 = 280 Example II Minor and Major rcs & rc ddition Postulate 1. Minor rc: + = 2. Major rc + = m = m + m m = m + m = = = 130 = 270 Example III entral ngles and rc ddition Postulate Let and be opposite rays and m = 75. Find 1. m 2. m 3. m = m m = m = m = = 75 = 105 = G F 80 E 40 o 90 o 75 o 4. m 5. m = m = m + m or m m = 180 = = 255 = 255 4

5 pril 26, 2013 T 128 P T is a diameter entral ngles - lasswork your turn Find the measure of each arc below, in circle P. 1. T 2. T 3. T 4. T T T 10. T T T T T T T T entral ngles - Homework Pull 1. Find the measure of the central angle that intercepts an arc with a degree measure of 35 o. Pull 2. Find the measure of the arc intercepted by a central angle with a measure of 120 o. In 3 10, the endpoints of are on circle, m = 89, and m = 42. Find each measure. 3. m 4. m 5. m 6. m 7. m 8. m 89 o 42 o 9. m 10. m Homework #'s

6 ttachments pg60.pdf irclengles.gsp