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Name:___________________________________ M1 Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Period:________ Date:_____________ GEOMETRY Lesson 4: Construct a Perpendicular Bisector Classwork Opening Exercise 1. An angle is called _______________________________ if its measure is 90˚. 2. Two lines are _______________________________ if they intersect in one point, and any of the angles formed by the intersection of the lines is a 90˚ angle. Two segments or rays are _________________________ if the lines containing them are ________________________________ lines. 3. A point is said to be _______________________from two different points and if . A point be _________________________ from a point and a line if the distance between and is equal to . is said to Lesson A perpendicular bisector of a segment passes through the _____________________ of the segment and forms _____________________ with the segment. We now investigate how to construct a perpendicular bisector of a line segment using a compass and straightedge. Using what you know about the construction of an angle bisector, experiment with your construction tools and the following line segment to establish the steps that determine this construction. A B Precisely describe the steps you took to bisect the segment. 1. Draw ________________ using radius _____________. 2. Draw ________________ using radius _____________. 3. Label the intersections of ________________ and _________________ points C and D. 4. Draw __________________ with a straight-edge. 5. Label the _________________________ of ̅̅̅̅ and ̅̅̅̅ point M, the __________________ of ̅̅̅̅ . Lesson 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Construct a Perpendicular Bisector 9/15/14 S.18 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ M1 Period:________ Date:_____________ GEOMETRY Now that you are familiar with the construction of a perpendicular bisector, we must make one last observation. Using your ruler, measure the following pairs of segments: I. Length of ̅̅̅̅ = ________, Length of ̅̅̅̅ = ________ II. Length of ̅̅̅̅ = ________, Length of ̅̅̅̅ = ________ III. Length of ̅̅̅̅ = ________, Length of ̅̅̅̅ = ________ C D Based on your findings, fill in the observation below. Observation: B A Any point on the perpendicular bisector of a line segment is E _____________________ from the endpoints of the line segment. Mathematical Modeling Exercise You know how to construct the perpendicular bisector of a segment. Now you will investigate how to construct a perpendicular to a line from a point not on . Think about how you have used circles in constructions so far and why the perpendicular bisector construction works the way it does. The first step of the instructions has been provided for you. Discover the construction and write the remaining steps. A Lesson 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Construct a Perpendicular Bisector 9/15/14 S.19 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Step 1. Draw circle so that the circle intersects line M1 Period:________ Date:_____________ GEOMETRY in two points. Step 2. Label the ________________________of circle A and line points B and C Step 3. Draw ______________________________________________________________________________________. Step 4. Draw ______________________________________________________________________________________. Step 5. Label ______________________________________________________________________________________. Step 6. Draw ______________________________________________________________________________________. Step 7. Label ______________________________________________________________________________________. BONUS….. give this one a try! 1. During this lesson, you constructed a perpendicular line to a line to use that construction to construct parallel lines: To construct parallel lines and from a point not on . We are going : I. Construct a perpendicular line to a line II. Construct a perpendicular line to from a point not on . through point . A Lesson 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Construct a Perpendicular Bisector 9/15/14 S.20 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ M1 Period:________ Date:_____________ GEOMETRY Lesson 4: Construct a Perpendicular Bisector Homework 2. Construct the perpendicular bisector of ̅̅̅̅ , ̅̅̅̅ , and ̅̅̅̅ on the triangle below. What do you notice about the segments you have constructed? A B C Lesson 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Construct a Perpendicular Bisector 9/15/14 S.21 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ 3. M1 Period:________ Date:_____________ GEOMETRY Two homes are built on a plot of land. Both homeowners have dogs, and are interested in putting up as much fencing as possible between their homes on the land, but in a way that keeps the fence equidistant from each home. Use your construction tools to determine where the fence should go on the plot of land. H2 H1 How will the fencing alter with the addition of a third home? H2 H1 H3 Lesson 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Construct a Perpendicular Bisector 9/15/14 S.22 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.