Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
Approximations of π wikipedia , lookup
Problem of Apollonius wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Name: ___________________________________ Date: _________________ THE ANGLE THEOREMS- DAY 1 GEOMETRY N All angle problems within circle geometry can essentially be classified into three subcategories: (1) angles within a circle, (2) angles on a circle, and (3) angles formed outside the circle. Theorem #1 – Any central angle formed (an angle with its vertex at the center of the circle) has a measure equal to the arc that it intercepts. Exercise #1: In the following diagram of circle O it is given that mAOB 112 . Find mAB . A O B Theorem #2 – An inscribed angle on a circle always measures one-half of its intercepted arc. Exercise #2: In the figure shown, it is given that mAB 160 . A (a) Determine mAOB . O (b) Determine mACB . C B Exercise #3: In the figure shown, BAC is the diameter of A and intersects with tangent ED at C. Find the measure of BCE . E B . A C D Theorem #3- The intersection of a radius or a diameter and a tangent always forms a right angle at the point of tangency. **NOTE: All of the arcs in a circle sum to 360O.** 1. Find each of the following in circle P. K a) mKPV = _________ b) m KZ = _________ c) mSPW = ________ d) m YVK = ________ e) m WSZ = _________ f) SPZ = _________ g) h) m VWY = ________ Z S P 52 V W 32 Y m SYK = _________ 2. Find mST in Circle P. S T P c° (3c–12)° W 3. Find the missing measurements 128° a) mD _________ b) k _________ i° 130° C mAB ________ f _________ k° mBD ________ i _________ mDA ________ e _________ g ________ f° g°