PPT-Measuring angles using full-circle protractors

Goal To learn how to measure angles using fullcircle protractors Now lets review what we know about angles What are the names of the different parts of an angle How do we measure angles using the halfcircle protractor. Circle Theorems. Dr J Frost (jfrost@tiffin.kingston.sch.uk. ). www.drfrostmaths.com. . Last modified: . 31. st. August 2015. RECAP. : Parts of a Circle. Sector. (Minor). Segment. Diameter. Radius. Tangent. Recognising different types of angles. What type of angle is this?. Right angle. What type of angle is this?. acute. What type of angle is this?. obtuse. What type of angle is this?. acute. What type of angle is this?. Central Angles. Central Angle. (of a circle). Central Angle. (of a circle). NOT A. Central Angle. (of a circle). A . central angle. is an angle whose vertex is the CENTER of the circle. CENTRAL ANGLES AND ARCS. 14. 2. . 7. 50. 8. 10. a) CE. b) DE. . c) angle CEB. . d) angle DEA. The Center of the circle. 6. . 5.4. . 8.9. 12.5. 9.9. 20.8. 108. 90. 123.9 or 124. a) PL. b) PM. c) All radii of a circle are congruent. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle . The three cases. We have to consider three cases. When arc PQ is minor arc . Double Angle. Triangles inside Circles. Angles connected by a . chord. Tangents to a circle. Cyclic Quadrilaterals. 2x. x. This is the ARC. o. Centre of Circle. The Angle . x. subtended at the centre of a circle by an arc is twice the size of the angle on the circumference subtended by the same arc.. Hubarth. Geometry. 10.7 Measure . of an Inscribed Angle. .. C. A. B. D. Ex 1 Use Inscribed Angles. a.. m. . T.  . mQR. b.. Find the indicated measure in. . P. .. M T = . mRS. =. . Identifying, Describing, and Applying Theorems about Circles. Understand and apply theorems about circles. G-C.2, Identify and describe relationships among inscribed angles, radii, and chords. . Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.. Angle . Notation – Three Possibilities. A. B. C. Vertex. Congruent Angles & Angle Measure. 30˚. A. B. C. D. E. Angle Bisector. A. B. C. D. “ If . . bisects. . .  . Using your Protractor. Wheel . of Formulas. Central Angle. Vertex ON circle. Vertex INSIDE circle. Vertex OUTSIDE circle. Arc Angle . Formulas. P. A. B. C. Case I:. . Vertex is . AT. the center. Case II:. . Vertex is . ON. Angles & Their Names. Angle: consists of two different rays with the same endpoint.. Sides: the rays of the angle.. Vertex: the endpoint of the angle.. Name the 3 angles.. or. or. or.  . Angles & Their Measures. 1. 2.. Now put it all together to solve for the missing angle.. Unit 6 – Day 3. Inscribed and Circumscribed. Today’s Objectives. Students will use properties of Central angles and Tangent lines to solve for missing parts. Measure angles with a protractor. Identify and use the angle addition postulate. Warm-Up: . Find the indicated value. AC = 20; AB = _____. A. B. C. x-4. 2x 3. Vocabulary:. Degree:. The most common unit of angle measure.. ). www.drfrostmaths.com. . Last modified: . 31. st. August 2015. RECAP. : Parts of a Circle. Sector. (Minor). Segment. Diameter. Radius. Tangent. Chord. (Minor) Arc. Circumference. ?. ?. ?. ?. ?. !.