The document discusses using perpendicular bisectors to solve geometry problems. It provides examples of finding lengths of line segments using the fact that the perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, it is equidistant from the endpoints. The document also discusses using the concurrent perpendicular bisectors of a triangle to find the point equidistant from the three vertices, which can be used to position a distributor equally from multiple locations. Guided practice questions apply these concepts, asking learners to find lengths, explain why a point is on a bisector, and locate a distributor point.

1. 5.2 Use Perpendicular Bisectors
5.2
Bell Thinger
1. Solve 3x = 8x – 15.
ANSWER
3
2. Solve 6x + 3 = 8x – 14.
ANSWER
8.5
3. If M is the midpoint of AB, AM = 5x – 2, and MB = 3x + 6,
find AB.
ANSWER
36

2. 5.2

3. 5.2

4. Example 1
5.2
ALGEBRA BD is the perpendicular
bisector of AC . Find AD.
SOLUTION
AD = CD
Perpendicular Bisector Theorem
5x = 3x + 14
Substitute.
x=7
AD = 5x = 5(7) = 35
Solve for x.

5. Example 2
5.2
In the diagram, WX is the
perpendicular bisector of YZ .
a. What segment lengths in the
diagram are equal?
SOLUTION
a. WX bisects YZ , so XY = XZ. Because W is on the
perpendicular bisector of YZ, WY = WZ by Theorem
5.2. The diagram shows that VY = VZ = 25.

6. Example 2
5.2
In the diagram, WX is the
perpendicular bisector of YZ .
b. Is V on WX ?
SOLUTION
b. Because VY = VZ, V is equidistant from Y and Z. So,
by the Converse of the Perpendicular Bisector
Theorem, V is on the perpendicular bisector of YZ ,
which is WX .

7. Guided Practice
5.2
In the diagram, JK is the
perpendicular bisector of NL.
1. What segment lengths are equal?
Explain your reasoning.
ANSWER
NJ =LJ since JK bisects NL. NK = LK by the
Perpendicular Bisector Theorem and the diagram
shows ML = MN.

8. Guided Practice
5.2
In the diagram, JK is the
perpendicular bisector of NL.
2. Find NK.
ANSWER
13

9. Guided Practice
5.2
In the diagram, JK is the
perpendicular bisector of NL.
3. Explain why M is on JK .
ANSWER
Since ML = MN, M is equidistant from N and
L, so by the Converse of the Perpendicular
Bisector Theorem M is on the perpendicular
bisector of NL which is JK.

10. 5.2

11. 5.2

12. 5.2

13. Example 3
5.2
FROZEN YOGURT
Three snack carts sell frozen
yogurt from points A, B, and C
outside a city. Each of the three
carts is the same distance from
the frozen yogurt distributor.
Find a location for the
distributor that is equidistant
from the three carts.

14. Example 3
5.2
SOLUTION
Theorem 5.4 shows you that you can find a point
equidistant from three points by using the perpendicular
bisectors of the triangle formed by those points.
Copy the positions of points A, B,
and C and connect those points to
draw ABC. Then use a ruler and
protractor to draw the three
perpendicular bisectors of ABC.
The point of concurrency D is the
location of the distributor.

15. Guided Practice
5.2
4. WHAT IF? Hot pretzels are sold
from points A and B and also
from a cart at point E. Where
could the pretzel distributor be
located if it is equidistant from
those three points? Sketch the
triangle and show the location.
ANSWER
Where the perpendicular
bisectors of the triangle
formed by A, B, and E
intersect

16. Exit Slip
5.2
In Exercises 1 and 2, find AB.
1.
ANSWER 25

17. Exit Slip
5.2
In Exercises 1 and 2, find AB.
2.
ANSWER 24.5

18. Exit Slip
5.2
3.
In this diagram, the perpendicular bisectors
of ABC meet at point G. Find EC and GC.
ANSWER 5; 7

19. 5.2