1. 1. Solve 3x = 8x – 15.
ANSWER 3
2. Solve 6x + 3 = 8x – 14.
ANSWER
8.5

2. 3. If M is the midpoint of AB, AM = 5x – 2, and MB = 3x + 6, find AB.
ANSWER 36

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

4. EXAMPLE 2
Use perpendicular bisectors
In the diagram, WX is the perpendicular bisector of YZ . a.
What segment lengths in the diagram are equal? b.
Is V on WX ?
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. 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 .

5. GUIDED PRACTICE
for Examples 1 and 2
In the diagram, JK is the perpendicular bisector of NL . 1.
What segment lengths are equal? Explain your reasoning.
NJ =LJ since JK bisects NL. NK = LK by the Perpendicular Bisector Theorem and the diagram shows ML = MN.
ANSWER

6. GUIDED PRACTICE
for Examples 1 and 2
In the diagram, JK is the perpendicular bisector of NL . 2.
Find NK. 13
ANSWER

7. GUIDED PRACTICE
for Examples 1 and 2
In the diagram, JK is the perpendicular bisector of NL . 3.
Explain why M is on JK .
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.
ANSWER

8. EXAMPLE 3
Use the concurrency of perpendicular bisectors
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.
FROZEN YOGURT
Find a location for the distributor that is equidistant from the three carts.

9. EXAMPLE 3
Use the concurrency of perpendicular bisectors
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.

10. GUIDED PRACTICE
for Example 3 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
and show the location.
triangle
Where the perpendicular bisectors of the triangle formed by A, B, and C intersect
ANSWER

11. Daily Homework Quiz
In Exercises 1 and 2, find AB. 1.
ANSWER 25

12. Daily Homework Quiz 2.
ANSWER
24.5

13. Daily Homework Quiz
3. In this diagram, the perpendicular bisectors
of ABC meet at point G. Find EC and GC.
ANSWER
5; 7