Lesson 5
RSD Geometry Local MATHEMATICS CURRICULUM
Name:__________________________
Period:_______ Dates:____________
U6
GEOMETRY
Lesson 5: Construct a Perpendicular Bisector
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.
3. A point 𝐴 is said to be _______________________from two different points 𝐵 and 𝐶 if 𝐴𝐵 = 𝐴𝐶.
Relevant Vocabulary
Term
Definition
Perpendicular Lines
Two lines are perpendicular if they
intercept to form a right angle
( 90 degrees)
Perpendicular bisector of a
segment
Diagram
A perpendicular bisector of a segment
passes through the ______________ of the
segment and forms ____________
___________ with the segment.
Construction of a perpendicular bisector http://www.mathopenref.com/constbisectline.html
Example 1. Construct the perpendicular bisector of the given line segment
Name:__________________________
Example 2
U6
Lesson 5
RSD Geometry Local MATHEMATICS CURRICULUM
Period:_______ Dates:____________
̅̅̅̅
Construct the perpendicular bisector of 𝐴𝐵
A
GEOMETRY
B
Write down 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 ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐶𝐷 point M, the __________________ of ̅̅̅̅
𝐴𝐵 .
RSD Geometry Local MATHEMATICS CURRICULUM
Name:__________________________
Lesson 5
Period:_______ Dates:____________
̅̅̅̅ that goes through point 𝑃.
Example 3. Construct a line perpendicular to segment 𝐴𝐵
U6
GEOMETRY
Hint- Make point 𝑃 the midpoint (use
your compass to draw a circle with
center 𝑃)
Label the new points. Now construct
the Line perpendicular to the new
segment that has midpoint point 𝑷
̅̅̅̅ .
b. Now investigate how to construct a perpendicular to a line 𝒔𝒆𝒈𝒎𝒆𝒏𝒕 ̅̅̅̅̅̅
𝑨𝑩 from a point 𝑷 not on 𝑨𝑩
Step 1. Draw circle 𝑃: center 𝑃, with radius so that circle 𝑃 intersects̅̅̅̅̅
𝐴𝐵 in two points.
Step 2. _________________________________________________________________________________
Step 3 _________________________________________________________________________________
Step 4 _________________________________________________________________________________
Step 5 _________________________________________________________________________________
U6
Lesson 5
RSD Geometry Local MATHEMATICS CURRICULUM
Name:__________________________
Period:_______ Dates:____________
GEOMETRY
Lesson 5: Construct a Perpendicular Bisector
Problem set
1. Construct a perpendicular bisector of a line segment using a compass and straightedge.
A
B
Precisely describe the steps you took to bisect the segment.
1._______________________________________________________________________________________
2._______________________________________________________________________________________
3._______________________________________________________________________________________
2. Using a compass and straightedge, construct a segment perpendicular to ̅̅̅̅
𝐴𝐵 that goes through Point 𝐶
C
A
B