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Geometry - Semester 2 Mrs. Day-Blattner 2/10/2016 Agenda 2/10/2016 1) Turn in Vocab review sheet 2) Quiz - 8 write in the answers to the questions, 10 multiple choice - circle on the paper. Show all “work” - reasoning for ALL questions. 2pts for each part of a question. 3) Lesson 5: How can I fit a quadrilateral in a circle? Stations ABCD - individual 1st attempts 4) Homework Circles (lessons 1-4) 8 questions Show all your work, state the theorem you are using etc. 2 points per part of a question if work shown and it makes sense. Use extra paper if necessary. Semester 1 Review 10 questions - select the correct response from the options given. Circle the answer on the paper. Show your thinking/work for possible 2 points per question. Start Stations Packet when you have turned in the quiz. New vocabulary In the first oval for lesson 5 “ Inscribed polygon” Definition: A polygon is inscribed in a circle if all the vertices (corners) of the polygon lie on the circle. Draw your own example and a non example (draw a polygon that is NOT inscribed in a circle) Station A. Construct a rectangle such that all four vertices of the rectangle lie on the circle below. Given a circle and a rectangle, what must be true about the rectangle for it to be possible to inscribe a congruent copy of it in the circle? Station A. Given a circle and a rectangle, what must be true about the rectangle for it to be possible to inscribe a congruent copy of it in the circle? The diagonals of the rectangle have to be the length of the diameter of the circle. Station B. Construct a kite in the circle below, and explain the construction using geometry. https://www.mathsisfun.com/definitions/kite.html Station C The figure below shows a rectangle inscribed in a circle. a) List the properties of a rectangle. b) List all the symmetries this diagram possesses. c) List the properties of a square. d) List all the symmetries that a diagram of a square inscribed in a circle possesses. Station C The figure below shows a rectangle inscribed in a circle. a) List the properties of a rectangle. Opposite sides parallel and congruent four right angles diagonals congruent and bisect each other a)Station C b) List all the symmetries this diagram possesses. Opposite sides are congruent all four angles are congruent diagonals are congruent figure may be reflected onto itself across the perpendicular bisector of the sides of the rectangle -can rotate onto itself with either a 180 degree or 360 degree rotation, clockwise or counterclockwise Station C c) List the properties of a square. Opposite sides parallel all sides congruent four right angles diagonals congruent, bisect each other, and are perpendicular Station C d) List all the symmetries that a diagram of square inscribed in a circle possesses. Same as for rectangle PLUS all four sides are congruent, figure may be reflected onto itself across the diagonals, the figure may be rotated onto itself with either 90 degree or 270 degree rotation, either clockwise or counter clockwise Station D ● A rectangle is inscribed into a circle (ABCD). The rectangle is cut along one of its diagonals and reflected across that diagonal to form a kite (ABED). Draw the kite and its diagonal (AE). Find all the angles in this new diagram, given that the acute angle between the diagonals of the rectangle in the original diagram was 40 degrees. Station D Possible diagram E B A C 40° D Station D cont. ● Given measure of angle ADB = 40 degrees ● then measure angle BDE = 40 degrees ● measure angle BAD = measure angle BED = 90 degrees (BD is a diameter of circle) ● measure angle ABD = measure angle EBD = 50 degrees ● measure angle ABE = 100 degrees ● measure angle ADE = 80 degrees Station - Challenge! ● With a partner Homework Packet of papers with headings: Station A, Station B, Station C and Station D. Use your textbook to help - look up the definition of a kite, remind yourself of all properties of a rectangle and square. Use pencil. Problem Set. (page 31 and 32, really difficult to read, S.19, S. 20 easier) 1- 6 - please write out the answer for problem 2 on separate lined paper.