Download Lesson 4: Construct a Perpendicular Bisector

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
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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.