Download Homework: Segment and angles: bisectors and midpoints

Name:______________________
September 28, 2012
Geometry
Homework: segment and angle bisectors
Homework: Segment and angles: bisectors and midpoints
Vocabulary-Directions: Complete each statement.
1. The ________of a segment is the point on the segment that divides it into two congruent segments.
2. A __________ is a segment, ray, line, or plane that intersects a segment at its midpoint.
3. To _________ a segment means to divide the segment into two congruent segments.
4. In geometry, segments that have the same length are called______________segments.
5. In geometry, angles that have the same measure are called _______________angles.
Directions: Draw the midpoint of each segment. Then use the midpoint ( averages) formula to confirm
your answer.
6.
M=_______________
7.
M=_________________
Name:______________________
September 28, 2012
Geometry
Homework: segment and angle bisectors
Directions: First draw each segment on the coordinate plane. Then use the midpoint formula to find the
coordinates of the midpoint of
8. P(0, 0), Q(6, -4)
M=_________
9. P(0, 8), Q(2, 6)
M=_________
.
Name:______________________
September 28, 2012
10. P(1, 2), Q(-5, 0)
M=_________
Geometry
Homework: segment and angle bisectors
Name:______________________
September 28, 2012
Geometry
Homework: segment and angle bisectors
Directions: For problem 11, show your work and/or explain how you got your answer for each part of the
problem. You can use the grid below:
11. Abria drew a segment PR that had one endpoint P (0, 2) and a midpoint M (4, 5).
a. Plot points P and M on the coordinate plane.
b. What is the horizontal distance (difference in x – values) of points P and M? Show or explain how you
got your answer.
c. What is the vertical distance (difference in y – values) of points P and M? Show or explain how you got
your answer.
d. Use your answers to parts b and c to find R, the other endpoint of Abria’s segment. Plot this point on
your graph. What are the coordinates of R? Show or explain how you got your answer.
R = ___________
Name:______________________
September 28, 2012
Directions:
Geometry
Homework: segment and angle bisectors
bisects PQR. Find the angle measure.
12.
13.
Directions: ABC is bisected by
15.
14.
Find the value of x.
16.
17.
Directions: Use the figure at right to complete each of the following statements.
18. If ∠KJM
MJL, then _______ is an angle bisector.
19. If
bisects KJL, then m ______
20. If
bisects KJL and m MJL = 48, then m _______= 48.
21.
m __?__.
bisects KJL and m KJM = 46, then m KJL = _______.
Name:______________________
September 28, 2012
Geometry
Homework: segment and angle bisectors
Directions: For problem 22, show your work and/or explain how you got your answer for each part of the
problem.
22. Aaron drew and measured
.m
= 70.
a. Sketch and label Aaron’s angle.
b. Aaron added angle bisector
. Add the angle bisector to your sketch.
c. Without measuring, Aaron found the measure of
how you got your answer.
What is the measure of
? Show or explain