Midpoints and Segment Bisectors - McBroom
Midpoints & Segment Bisectors Name_______________________
Activity
I. Midpoint
1. Trace segment AB onto a piece of patty paper.
2. Fold one endpoint of AB onto the other and crease.
Label the creased point C.
3. Make a conjecture about AC and BC.
4. A point is the midpoint of a segment if and only if
II. Segment Bisectors
5. Study the diagrams below and write a definition of a segment bisector.
6. A segment bisector is
7. Complete the following statements.
a) MR = 24, HR = ______ b) TR = 16, AT = ______
c) MH = 58, MR = ______
d) R is the midpoint of ______ and ______.
III. Practices
8. M is the midpoint of PQ. PM = 7x + 8 and MQ = 5x+ 20. Draw the diagram.
x= PM= ___ MQ = _ PQ =
9. B is the midpoint of AC. AB = 2x – 1 and AC = 3x+ 2. Draw the diagram.
x= AB= ___ BC = _ AC =
10. Given JB is the segment bisector of AD,
AD = 24, AZ = 2x + 4, and m(JZA= 3y,
Find the value of x and y.
Use Figure 2 for problems 11 – 13.
11. What is the midpoint of AB?
12. What is the coordinate of the midpoint of QB?
13. The coordinate of the midpoint of AR is -5.
What is the coordinate of point R?
Use Figure 3 for problems 15 – 16.
14. If TM = 3x + 5, MQ = x + 17, find the value of x.
15. If AM = 5y – 1, AB = 38, find the value of y.
Midpoints & Segment Bisectors Name
Worksheet Period
Draw a diagram for each problem.
1. M is the midpoint of PQ. PM = 6x + 7 and MQ = 9x – 8, find the length of PQ.
2. M is the midpoint of PQ. PM = 5x + 8 and PQ = 76, find x.
3. M is the midpoint of PQ. PM = 9x + 3 and MQ = 11x – 17, find x and PQ.
4. M is the midpoint of PQ. MQ = 5x + 8 and PQ = 6x + 56, find PM.
5. DE bisects AB at C. If AC = 8x – 3 and CB = 4x + 57, find x.
6. A is the midpoint of CT. CA = 2x + 8 and AT = 4x + 2, find x and length of CT.
7. A is the midpoint of CT. CA = 7x – 5, CT = 46, find x.
8. A is the midpoint of CT. CA = 3x + 6 and CT = 24, find x.
9. DE bisects AB at C. If AC = 8x – 23 and CB = 3x + 22, find x.
-----------------------
A
B
3
5
21
20
3
3
3
1.5
1.5
Segment Bisectors
Not Segment Bisectors
M
H
A
T
R
J
B
A
D
Z
W
A
S
Q
B
-8
0
2
4
8
Figure 2
T
B
A
M
Q
Figure 3
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