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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