1.4. Midpoints and Segment Bisectors http://www.ck12.org
Guided Practice
- Which line is the perpendicular bisector ofMN?
- Findxandy.
- Find the midpoint between (3, 7) and (7, 11)
Answers:
- The perpendicular bisector must bisectMNand be perpendicular to it. Only
←→
OQsatisfies both requirements.←→
SR
is just a bisector.
The line shown is the perpendicular bisector. So, 3x− 6 = 21 , 3 x= 27 ,x=9. And,( 4 y− 2 )◦= 90 ◦, 4 y◦=
92 ◦,y= 23 ◦.
(
3 + 7
2
,
7 + 11
2
)
=
(
10
2
,
18
2
)
= ( 5 , 9 )
.
Practice
- Copy the figure below and label it with the following information:
(^6) A∼= (^6) C
(^6) B∼= (^6) D
AB∼=CD
AD∼=BC
For 2-9, find the lengths, given:His the midpoint ofAEandDG,Bis the midpoint ofAC,GDis the perpendicular
bisector ofFAandEC,AC∼=F E,andFA∼=EC.
2.AB
3.GA
4.ED
5.HE
6.FA
7.GD
- How many copies of triangleAHBcan fit inside rectangleF ECAwithout overlapping?
9.ConstructionUsing your ruler, draw a line segment that is 7 cm long. Then use your compass to construct
the perpendicular bisector, What is the measure of each segment?
10.ConstructionUsing your ruler, draw a line segment that is 4 in long. Then use your compass to construct the
perpendicular bisector, What is the measure of each segment?
For questions 10-13, find the midpoint between each pair of points.
- (-2, -3) and (8, -7)
- (9, -1) and (-6, -11)
- (-4, 10) and (14, 0)
- (0, -5) and (-9, 9)