Eureka Math™ Geometry Module Student File_B Additional Student Materials This file contains: • Geo-M1 Exit Tickets1 • Geo-M1 Mid-Module Assessment • Geo-M1 End-of-Module Assessment 1Note that Lesson of this module does not include an Exit Ticket Published by Great Mindsđ Copyright â 2015 Great Minds No part of this work may be reproduced, sold, or commercialized, in whole or in part, without written permission from Great Minds Non-commercial use is licensed pursuant to a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license; for more information, go to http://greatminds.net/maps/math/copyright Printed in the U.S.A This book may be purchased from the publisher at eureka-math.org 10 Geo-M1-SFB-1.3.2-05.2016 Exit Ticket Packet Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name _ Date Lesson 1: Construct an Equilateral Triangle Exit Ticket We saw two different scenarios where we used the construction of an equilateral triangle to help determine a needed location (i.e., the friends playing catch in the park and the sitting cats) Can you think of another scenario where the construction of an equilateral triangle might be useful? Articulate how you would find the needed location using an equilateral triangle Lesson 1: Construct an Equilateral Triangle ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name _ Date Lesson 2: Construct an Equilateral Triangle Exit Ticket ᇞ ܥܤܣis shown below Is it an equilateral triangle? Justify your response Lesson 2: Construct an Equilateral Triangle ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name _ Date Lesson 3: Copy and Bisect an Angle Exit Ticket Later that day, Jimmy and Joey were working together to build a kite with sticks, newspapers, tape, and string After they fastened the sticks together in the overall shape of the kite, Jimmy looked at the position of the sticks and said that each of the four corners of the kite is bisected; Joey said that they would only be able to bisect the top and bottom angles of the kite Who is correct? Explain Lesson 3: Copy and Bisect an Angle ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name _ Date Lesson 4: Construct a Perpendicular Bisector Exit Ticket Divide the following segment ܤܣinto four segments of equal length Lesson 4: Construct a Perpendicular Bisector ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name Date Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point Exit Ticket Use the following diagram to answer the questions below: a Name an angle supplementary to ܬܼܪס, and provide the reason for your calculation b Name an angle complementary to ܬܼܪס, and provide the reason for your calculation If ݉ = ܬܼܪס38°, what is the measure of each of the following angles? Provide reasons for your calculations a ݉ܩܼܨס b ݉ܩܼܪס c ݉ܬܼܣס Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name Date Lesson 7: Solving for Unknown Angles—Transversals Exit Ticket Determine the value of each variable =ݔ =ݕ =ݖ Lesson 7: Solve for Unknown Angles—Transversals ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name Date Lesson 8: Solve for Unknown Angles—Angles in a Triangle Exit Ticket Find the value of ݀ and ݔ ݀ = = ݔ Lesson 8: Solve for Unknown Angles—Angles in a Triangle ©2015 Great Minds eureka-math.org Lesson A STORY OF FUNCTIONS M1 GEOMETRY Name Date Lesson 9: Unknown Angle Proofs—Writing Proofs Exit Ticket In the diagram to the right, prove that the sum of the labeled angles is 180° Lesson 9: Unknown Angle Proofs—Writing Proofs ©2015 Great Minds eureka-math.org Assessment Packet Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY Name Date State precise definitions of angle, circle, perpendicular, parallel, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc Angle: Circle: Perpendicular: Parallel: Line segment: Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY A rigid motion, ܬ, of the plane takes a point, ܣ, as input and gives ܥas output (i.e., )ܥ = )ܣ(ܬ Similarly, ܦ = )ܤ(ܬfor input point ܤand output point ܦ തതതത ؆ ܦܤ തതതത because rigid motions Jerry claims that knowing nothing else about ܬ, we can be sure that ܥܣ preserve distance a Show that Jerry’s claim is incorrect by giving a counterexample (hint: a counterexample would be a specific rigid motion and four points ܣ, ܤ, ܥ, and ܦin the plane such that the motion takes ܣto ܥ തതതത ؈ ܦܤ തതതത) and ܤto ܦ, yet ܥܣ b There is a type of rigid motion for which Jerry’s claim is always true Which type below is it? Rotation c Reflection Translation തതതത Would this be true for any rigid motion that satisfies the Suppose Jerry claimed that തതതത ܤܣ؆ ܦܥ conditions described in the first paragraph? Why or why not? Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY a In the diagram below, ݈ is a line, ܣis a point on the line, and ܤis a point not on the line ܥis the തതതത Show how to create a line parallel to ݈ that passes through ܤby using a rotation midpoint of ܤܣ about ܥ b Suppose that four lines in a given plane, ݈ ଵ, ݈ ଶ, ݉ଵ, and ݉ଶ are given, with the conditions (also given) that ݈ ଵ ݈ צଶ, ݉ଵ ݉ צଶ, and ݈ ଵ is neither parallel nor perpendicular to ݉ଵ i Sketch (freehand) a diagram of ݈ ଵ, ݈ ଶ, ݉ଵ, and ݉ଶ to illustrate the given conditions ii In any diagram that illustrates the given conditions, how many distinct angles are formed? Count only angles that measure less than 180°, and count two angles as the same only if they have the same vertex and the same edges Among these angles, how many different angle measures are formed? Justify your answer Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY In the figure below, there is a reflection that transforms ᇞ ܥܤܣto ᇞ ܣԢܤԢܥԢ Use a straightedge and compass to construct the line of reflection, and list the steps of the construction Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY Precisely define each of the three rigid motion transformations identified a ( ) ܶ ሬሬሬሬሬԦ ܲ _ b ݎ (ܲ) c ܴ ,ଷι (ܲ) _ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org Mid-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY തതതത and of ܦܥ തതതത Given in the figure below, line ݈ is the perpendicular bisector of ܤܣ a തതതത ؆ ܦܤ തതതത using rigid motions Show ܥܣ b Show ܦܥܣס؆ ܥܦܤס c തതതത Show തതതത ܦܥ צ ܤܣ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY Name Date Each of the illustrations on the next page shows in black a plane figure consisting of the letters F, R, E, and D evenly spaced and arranged in a row In each illustration, an alteration of the black figure is shown in gray In some of the illustrations, the gray figure is obtained from the black figure by a geometric transformation consisting of a single rotation In others, this is not the case a Which illustrations show a single rotation? b Some of the illustrations are not rotations or even a sequence of rigid transformations Select one such illustration, and use it to explain why it is not a sequence of rigid transformations Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY തതതത bisects Әܤܥܣ, ܥܤ = ܤܣ, ݉Ә = ܥܧܤ90°, and ݉Ә = ܧܥܦ42° In the figure below, ܦܥ Find the measure of Әܣ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY തതതത is the angle bisector of ܥܣܤס തതതതതത തതതതതത are straight lines, and ܦܣ തതതത ܥܲ צ തതതത In the figure below, ܦܣ ܲܣܤand ܥܦܤ Prove that ܥܣ = ܲܣ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY തതതത , ܥܣ തതതത ؆ ܨܦ തതതത , and ܣס؆ ܦס ᇞ ܥܤܣand ᇞ ܨܧܦ, in the figure below are such that തതതത ܤܣ؆ ܧܦ a Which criteria for triangle congruence (ASA, SAS, SSS) implies that ᇞ ܥܤܣ؆ᇞ ?ܨܧܦ b Describe a sequence of rigid transformations that shows ᇞ ܥܤܣ؆ᇞ ܨܧܦ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY a തതതത List the steps of the construction Construct a square ܦܥܤܣwith side ܤܣ Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY b Three rigid motions are to be performed on square ܦܥܤܣ The first rigid motion is the reflection through തതതത ܦܤ The second rigid motion is a 90° clockwise rotation around the center of the square Describe the third rigid motion that will ultimately map ܦܥܤܣback to its original position Label the image of each rigid motion ܣ, ܤ, ܥ, and ܦin the blanks provided തതതത Rigid Motion Description: Reflection through ܦܤ Rigid Motion Description: 90° clockwise rotation around the center of the square Rigid Motion Description: Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org End-of-Module Assessment Task A STORY OF FUNCTIONS M1 GEOMETRY തതതത and ܦܥ തതതത, respectively Suppose that ܦܥܤܣis a parallelogram and that ܯand ܰ are the midpoints of ܤܣ Prove that ܰܥܯܣis a parallelogram Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org ... OF FUNCTIONS M1 GEOMETRY Name _ Date Lesson 15: Rotations, Reflections, and Symmetry Exit Ticket What is the relationship between a rotation and a reflection?... Reflection through ܦܤ Rigid Motion Description: 90° clockwise rotation around the center of the square Rigid Motion Description: Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org... transformations Select one such illustration, and use it to explain why it is not a sequence of rigid transformations Module 1: Congruence, Proof, and Constructions ©2015 Great Minds eureka-math.org