5.2

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Use Perpendicular Bisectors

5.2 Warm-Up

1. Solve 3x = 8x – 15.

ANSWER 3

ANSWER 8.5

2. Solve 6x + 3 = 8x – 14.

ANSWER 36

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

5.2 Example 1

AD = CD Perpendicular Bisector Theorem

3x + 145x = Substitute.

7x = Solve for x.

BD is the perpendicular bisector of AC . Find AD.ALGEBRA

AD = 5x = 5(7) = 35

SOLUTION

5.2 Example 2

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.

In the diagram, WX is the perpendicular bisector of YZ .

5.2 Example 2

SOLUTION

In the diagram, WX is the perpendicular bisector of YZ .

b. Is V on WX ?

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 .

5.2 Guided Practice

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

5.2 Guided Practice

In the diagram, JK is the perpendicular bisector of NL.

2. Find NK.

13ANSWER

5.2 Guided Practice

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

5.2 Example 3

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.

5.2 Example 3

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.

SOLUTION

5.2 Guided Practice

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.

Where the perpendicular bisectors of the triangle formed by A, B, and E intersect

ANSWER

5.2 Lesson Quiz

In Exercises 1 and 2, find AB.

1.

ANSWER 25

5.2 Lesson Quiz

In Exercises 1 and 2, find AB.

2.

ANSWER 24.5

5.2 Lesson Quiz

3. In this diagram, the perpendicular bisectorsof ABC meet at point G. Find EC and GC.

ANSWER 5; 7