1. Bell Ringer

2. Angle Bisector and Perpendicular Bisector

3. Distance From A Point to A Line
The distance from a point to a line is measured by the length of the perpendicular segment from a point to the line. :

4. Equidistant
Equidistant is when a point is the same distance from one line as it is from another line, the point is equidistant from the two lines. :

5. Use the Angle Bisector Theorem
Example 1
Use the Angle Bisector Theorem
Prove that ∆TWU  ∆VWU.
∆TWU  ∆VWU.
UW bisects TUV. ∆UTW and ∆UVW are right triangles.
SOLUTION
Statements
Reasons 1.
Given
UW bisects TUV.
Given 2.
∆UTW and ∆UVW are right triangles.
Reflexive Prop. of Congruence 3.
WU  WU
Angle Bisector Theorem 4.
WV  WT
HL Congruence Theorem 5.
∆TWU  ∆VWU

6. Perpendicular Bisector
Perpendicular A segment, ray, or line that is perpendicular to a segment at its midpoint. :

7. Use Perpendicular Bisectors
Example 2
Use Perpendicular Bisectors
Use the diagram to find AB.
SOLUTION
In the diagram, AC is the perpendicular bisector of DB.
8x = 5x +12
By the Perpendicular Bisector Theorem, AB = AD.
3x = 12
Subtract 5x from each side. 2 3x 3 12 =
Divide each side by 3.
x = 4
Simplify.
You are asked to find AB, not just the value of x.
ANSWER
AB = 8x = 8 · 4 = 32

8. Now You Try  Use Angle Bisectors and Perpendicular Bisectors 1.
Find FH.
ANSWER 5 2.
Find MK.
ANSWER 20 3.
Find EF.
ANSWER 15

9. Use the Perpendicular Bisector Theorem
Example 3
Use the Perpendicular Bisector Theorem
In the diagram, MN is the perpendicular bisector of ST. Prove that ∆MST is isosceles.
SOLUTION
To prove that ∆MST is isosceles, show that MS = MT.
Statements
Reasons
Given 1.
MN is the bisector of ST. 
Perpendicular Bisector Theorem 2.
MS = MT
Def. of isosceles triangle 3.
∆MST is isosceles.

10. Now You Try 

11. Now You Try 

12. Page 276

13. Complete Page
#s & 32 even Only