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Warm-Up

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Warm-Up Use the figure below for Exercises 1 4. 1. If UV = 13, find RT. 2. If ST = 20, find UW. 26 10 34 in. 6 ANSWER ANSWER ANSWER ANSWER 4. If VW = 2x 4, and ... – PowerPoint PPT presentation

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Title: Warm-Up


1
Warm-Up
1. If UV 13, find RT.
2. If ST 20, find UW.
4. If VW 2x 4, and RS 3x 3, what is
VW?
5. Place a rectangle in a coordinate plane so
its vertical side has length a and its
horizontal side has width 2a. Label the
coordinates of each vertex.
2
Warm-Up
3
Perpendicular Bisector
  • A segment, ray, line or plane that is
    perpendicular to a segment at its midpoint is
    called a perpendicular bisector.
  • A point is equidistant from two figures if the
    point is the same distance from each figure.

4
Theorems to remember
  • In a plane, if a point is on the perpendicular
    bisector of a segment, then it is equidistant
    from the endpoints of the segment.
  • Converse In a plane, if a point is equidistant
    from the endpoints of a segment, then it is on
    the perpendicular bisector of the segment.

5
EXAMPLE 1
Use the Perpendicular Bisector Theorem
ALGEBRA
AD CD
Perpendicular Bisector Theorem
Substitute.
Solve for x.
6
EXAMPLE 2
Use perpendicular bisectors
b.
7
for Examples 1 and 2
GUIDED PRACTICE
8
for Examples 1 and 2
GUIDED PRACTICE
9
Concurrency
  • When three of more lines, rays, or segments
    intersect in the same point, they are called
    concurrent.
  • The point of intersection of the lines, rays, or
    segments is called the point of concurrency.

10
Concurrency of Perpendicular Bisectors of a
Triangle
  • The perpendicular bisectors of a triangle
    intersect at a point that is equidistant from the
    vertices of the triangle.

11
Circumcenter
  • The point of concurrency of the three
    perpendicular bisectors of a triangle is called
    the circumcenter of the triangle
  • Circumscribed Circle

12
EXAMPLE 3
Use the concurrency of perpendicular bisectors
FROZEN YOGURT
Find a location for the distributor that is
equidistant from the three carts.
13
EXAMPLE 3
Use the concurrency of perpendicular bisectors
14
for Example 3
GUIDED PRACTICE
15
Warm-Up
In Exercises 1 and 2, find AB.
16
Daily Homework Quiz
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