FL State Adoption Bid # 3704 Eureka Math™ Geometry Exit Ticket Packet Module 5 Topic A Topic C Lesson 1 Exit Ticket Qty: 30 Lesson 11 Exit Ticket Qty: 30 Lesson 2 Exit Ticket Qty: 30 Lesson 12 Exit Ticket Qty: 30 Lesson 3 Exit Ticket Qty: 30 Lesson 13 Exit Ticket Qty: 30 Lesson 4 Exit Ticket Qty: 30 Lesson 14 Exit Ticket Qty: 30 Lesson 5 Exit Ticket Qty: 30 Lesson 15 Exit Ticket Qty: 30 Lesson 6 Exit Ticket Qty: 30 Lesson 16 Exit Ticket Qty: 30 Topic B Topic D Lesson 7 Exit Ticket Qty: 30 Lesson 17 Exit Ticket Qty: 30 Lesson 8 Exit Ticket Qty: 30 Lesson 18 Exit Ticket Qty: 30 Lesson 9 Exit Ticket Qty: 30 Lesson 19 Exit Ticket Qty: 30 Lesson 10 Exit Ticket Qty: 30 Topic E Lesson 20 Exit Ticket Qty: 30 Lesson 21 Exit Ticket Qty: 30 Published by the non-profit Great Minds Copyright © 2015 Great Minds. All rights reserved. No part of this work may be reproduced or used in any form or by any means — graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems — without written permission from the copyright holder. “Great Minds” and “Eureka Math” are registered trademarks of Great Minds. Printed in the U.S.A. This book may be purchased from the publisher at eureka-math.org 10 9 8 7 6 5 4 3 2 1 ^dKZzK&&hEd/KE^ Lesson 1 M5 GEOMETRY Name Date Lesson 1: Thales’ Theorem Exit Ticket Circle ܣ is shown below. 1. Draw two diameters of the circle. 2. Identify the shape defined by the endpoints of the two diameters. 3. Explain why this shape is always the result. Lesson 1: Thales’ Theorem 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 2 M5 GEOMETRY Name Date Lesson 2: Circles, Chords, Diameters, and Their Relationships Exit Ticket 1. Given circle ܣ shown, ܣܨ ൌ ܣܩ and ܤܥ ൌ ʹʹ. Find ܦܧ. .തܧതതതܦ٣ തതതܤܣIn the figure, circle ܲ has a radius of ͳͲ. ത .2 a. If ܣܤ ൌ ͺ, what is the length of ܣܥതതതത? b. If ܦܥ ൌ ʹ, what is the length of തܣܤതതത? Lesson 2: Circles, Chords, Diameters, and Their Relationships 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 3 M5 GEOMETRY Name Date Lesson 3: Rectangles Inscribed in Circles Exit Ticket Rectangle ܣܤܥܦ is inscribed in circle ܲ. Boris says that diagonal ܣܥതതതത could pass through the center, but it does not have to pass through the center. Is Boris correct? Explain your answer in words, or draw a picture to help you explain your thinking. Lesson 3: Rectangles Inscribed in Circles 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 4 M5 GEOMETRY Name Date Lesson 4: Experiments with Inscribed Angles Exit Ticket Joey marks two points on a piece of paper, as we did in the Exploratory Challenge, and labels them ܣ and ܤ. Using the trapezoid shown below, he pushes the acute angle through points ܣ and ܤ from below several times so that the sides of the angle touch points ܣ and ܤ, marking the location of the vertex each time. Joey claims that the shape he forms by doing this is the minor arc of a circle and that he can form the major arc by pushing the obtuse angle through points ܣ and ܤ from above. “The obtuse angle has the greater measure, so it will form the greater arc,” states Joey. Ebony disagrees, saying that Joey has it backwards. “The acute angle will trace the major arc,” claims Ebony. 1. Who is correct, Joey or Ebony? Why? 2. How are the acute and obtuse angles of the trapezoid related? 3. If Joey pushes one of the right angles through the two points, what type of figure is created? How does this relate to the major and minor arcs created above? Lesson 4: Experiments with Inscribed Angles 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 5 M5 GEOMETRY Name Date Lesson 5: Inscribed Angle Theorem and Its Applications Exit Ticket has a measure of ͳͷ degrees, find the values of ݔ and ݕ. Explain how you ܤ The center of the circle below is ܱ. If angle know. Lesson 5: Inscribed Angle Theorem and Its Applications 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 6 M5 GEOMETRY Name Date Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles Exit Ticket .Find the measure of angles ݔ and ݕ. Explain the relationships and theorems used Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 7 M5 GEOMETRY Name Date Lesson 7: The Angle Measure of an Arc Exit Ticket Given circle ܣ with diameters തܤܥതതത and തܦܧതതത and ݉ܥ෢ܦ ൌ ͷ͸ι. a. Name a central angle. b. Name an inscribed angle. c. Name a chord that is not a diameter. ?ܦܣܥס d. What is the measure of ?ܦܤܥס e. What is the measure of f. Name ͵ angles of equal measure. g. What is the degree measure of ܥܦ෣ܤ? Lesson 7: The Angle Measure of an Arc 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 8 M5 GEOMETRY Name Date Lesson 8: Arcs and Chords Exit Ticket 1. Given circle ܣ with radius ͳͲ, prove ܤܧ ൌ ܦܥ. 2. Given the circle at right, find ݉ܤ෢ܦ. Lesson 8: Arcs and Chords 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 9 M5 GEOMETRY Name Date Lesson 9: Arc Length and Areas of Sectors Exit Ticket 1. Find the arc length of ܴܲܳ෣. 2. Find the area of sector ܱܴܲ. Lesson 9: Arc Length and Areas of Sectors 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 10 M5 GEOMETRY Name Date Lesson 10: Unknown Length and Area Problems Exit Ticket 1. Given circle ܣ, find the following (round to the nearest hundredth). a. ݉ܤ෢ܥ in degrees b. Area of sector ܤܣܥ 2. Find the shaded area (round to the nearest hundredth). ͸ʹι Lesson 10: Unknown Length and Area Problems 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 11 M5 GEOMETRY Name Date Lesson 11: Properties of Tangents Exit Ticket 1. If ܤܥ ൌ ͻ, ܣܤ ൌ ͸, and ܣܥ ൌ ͳͷ, is ܤܥശሬሬሬሬԦ tangent to circle ܣ? Explain. 2. Construct a line tangent to circle ܣ through point ܤ. Lesson 11: Properties of Tangents 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 12 M5 GEOMETRY Name Date Lesson 12: Tangent Segments Exit Ticket 1. Draw a circle tangent to both rays of this angle. Explain how you .ܤܥܣס and ܥܤܣס be the points of tangency of your circle. Find the measures of ܥ and ܤ Let .2 determined your answer. 3. Let ܲ be the center of your circle. Find the measures of the angles in ᇞܣܲܤ. Lesson 12: Tangent Segments 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 13 M5 GEOMETRY Name Date Lesson 13: The Inscribed Angle Alternate—A Tangent Angle Exit Ticket Find ܽ, ܾ, and ܿ. Lesson 13: The Inscribed Angle Alternate—A Tangent Angle 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 14 M5 GEOMETRY Name Date Lesson 14: Secant Lines; Secant Lines That Meet Inside a Circle Exit Ticket ͳ ൌ ሺͳʹ͵ሻ ൌ ͸ͳι because it is half of the intercepted arc. Sandra says that you cannot ܥܨܦס݉ Lowell says that .1 ʹ ?because you do not have enough information. Who is correct and why ܥܨܦס determine the measure of .ൌ ͻͻι, find and explain how you determined your answer ܥܨܧס݉ If .2 ܧܨܤס݉ .a b. ݉ܤ෢ܧ Lesson 14: Secant Lines; Secant Lines That Meet Inside a Circle 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 15 M5 GEOMETRY Name Date Lesson 15: Secant Angle Theorem, Exterior Case Exit Ticket .Find ݔι . Explain your answer .1 .ൌݕιെݔι. Justify your work ܩ෢ܨ݉ ൌݕι൅ݔι and ܧ෢ܦ݉ Use the diagram to show that .2 Lesson 15: Secant Angle Theorem, Exterior Case 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 16 M5 GEOMETRY Name Date Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant- Tangent) Diagrams Exit Ticket In the circle below, ݉ܩ෢ܨ ൌ ͵Ͳι, ݉ܦ෢ܧ ൌ ͳʹͲι, ܥܩ ൌ ͸, ܩܪ ൌ ʹ, ܨܪ ൌ ͵, ܥܨ ൌ Ͷ, ܪܧ ൌ ͻ, and ܨܧ ൌ ͳʹ. .(ܧܪܦס݉) ܽ a. Find .and explain your answer ,(ܧܥܦס݉) ܾ b. Find .and explain your answer ,(ܦܪ) c. Find ݔ .(ܩܦ) d. Find ݕ Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 17 M5 GEOMETRY Name Date Lesson 17: Writing the Equation for a Circle Exit Ticket .Describe the circle given by the equation ሺݔെ͹ሻଶ ൅ ሺݕെͺሻଶ ൌͻ .1 2. Write the equation for a circle with center ሺͲǡ െͶሻ and radius ͺ. 3. Write the equation for the circle shown below. 4. A circle has a diameter with endpoints at ሺ͸ǡ ͷሻ and ሺͺǡ ͷሻ. Write the equation for the circle. Lesson 17: Writing the Equation for a Circle 1 ©2015 Great Min ds. eureka-math.org (&0.&511 ^dKZzK&&hEd/KE^ Lesson 18 M5 GEOMETRY Name Date Lesson 18: Recognizing Equations of Circles Exit Ticket 1.