### Factors, Fractions, and Exponents

```Warm-Up:
EOC Prep
What is RS?
What is m<ABC?
Bisectors in
Triangles
5.2
Today’s Goals
By the end of class today, YOU should be able to…
1. Define and use the properties of
perpendicular bisectors and angle
bisectors to solve for unknowns.
2. Locate places equidistant from two given
points on a map.
Review…
We learned in chapter 4 that
≅ ΔCBD. Therefore, we can conclude that
CA ≅ CB, that CA = CB, or simply that C is
equidistant from points A and B.
Perpendicular Bisector
Theorem

If a point is on the perpendicular bisector
of a segment, then it is equidistant from
the endpoints of the segment.
Converse of the Perpendicular
Bisector Theorem

If a point is equidistant from the
endpoints of a segment, then it is on the
perpendicular bisector of the segment.
Ex.1: Using the Perpendicular
Bisector Theorem
If CD is the perpendicular bisector of
both XY and ST, and CY = 16. Find
the length of TY.
Ex.1: Solution
CS = CT
CY – CT = TY
We know from the Perpendicular Bisector
Theorem that CS is equivalent to CT
Subtract to find the value of TY
You Try…
If CD is the perpendicular bisector of
both XY and ST, and CY = 16. Find
the length of CX.
Angle Bisector Theorem

If a point is on the bisector of an angle,
then the point is equidistant from the
sides of the angle.
Converse of the Angle
Bisector Theorem

If a point in the interior of an angle is
equidistant from the sides of the angle,
then the point is on the angle bisector.
Ex.2: Using the Angle
Bisector Theorem
Find the value of x, then find FD and FB:
Ex.2: Solution
From the diagram we see that F is on the bisector of ACE. Therefore,
FB = FD.
FB = FD
5x = 2x + 24
Substitute
3x = 24
Subtract 2x
x=8
Divide by 3
FB = 5x = 5(8) = 40
Substitute
FD = 40
Substitute
You Try…
Does point A lie on an angle bisector of
<TXR? Explain.
Angle bisector constructions
Construct an angle ABC
Place the compass point on the angle vertex
with the compass set to any convenient width
Draw an arc that falls across both legs of the angle
*The compass can then be adjusted at this
point if desired
From where an arc crosses a leg, make an arc in the angle's
interior, then without changing the compass width, repeat for
the other leg
Draw a straight line from B to point D, where the arcs
cross
Done. The
line just drawn
bisects the angle ABC
Practice
A mysterious map has come into your
possession. The map shows the Sea Islands
off the coast of Georgia. But that’s not all!
The map also contains three clues that tell
where a treasure is supposedly buried!



The 1st clue: Draw a line from Baxley to Savannah. From Savannah, draw a
southwesterly line that forms a 60° angle with the first line. The treasure is
on an island that lies along the second line. On which islands could the
treasure be buried?
The 2nd clue: The treasure is on an island 22 miles from Everett. Construct
a figure that contains all the points 22 miles from Everett. According to the
first two clues, on which islands could the treasure be buried? Explain.
The 3rd clue: The perpendicular bisector of the line segment between Baxley
and Jacksonville passes through the island. The treasure is buried by the
lighthouse on that island. On which island is the treasure buried? Explain.
Homework
 Page
251 #s 8-11, 16, 18
 Page 252 # 30
 The
assignment can also be found at:
• http://www.pearsonsuccessnet.com/snpap
p/iText/products/0-13-037878-X/Ch05/0502/PH_Geom_ch05-02_Ex.pdf
```