Date post: | 18-Dec-2015 |
Category: |
Documents |
Upload: | hannah-dixon |
View: | 225 times |
Download: | 1 times |
Bell Ringer
Angle Bisector and Perpendicular Bisector
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.
:
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.
:
Use the Angle Bisector TheoremExample 1
HL Congruence Theorem5.∆TWU ∆VWU5.
Given2.2. ∆UTW and ∆UVW are right triangles.
Reflexive Prop. of Congruence3.3. WU WU
Angle Bisector Theorem4.4. WV WT
Prove that ∆TWU ∆VWU.
∆TWU ∆VWU.
UW bisects TUV.∆UTW and ∆UVW are right triangles.
SOLUTION
Statements Reasons
1. Given1. UW bisects TUV.
Perpendicular Bisector– Perpendicular A segment, ray, or line that is
perpendicular to a segment at its midpoint.
:
Use Perpendicular BisectorsExample 2
Use the diagram to find AB.
8x = 5x +12 By the Perpendicular Bisector Theorem, AB = AD.
3x = 12 Subtract 5x from each side.
2
3x3
12= Divide each side by 3.
x = 4 Simplify.
ANSWER AB = 8x = 8 · 4 = 32
You are asked to find AB, not just the value of x.
SOLUTION
In the diagram, AC is the perpendicular bisector of DB.
Now You Try Use Angle Bisectors and Perpendicular Bisectors
ANSWER 5
ANSWER 20
ANSWER 15
1. Find FH.
2. Find MK.
3. Find EF.
Use the Perpendicular Bisector TheoremExample 3
Def. of isosceles triangle3.∆MST is isosceles.3.
Perpendicular Bisector Theorem
2.2. MS = MT
SOLUTION
To prove that ∆MST is isosceles, show that MS = MT.
In the diagram, MN is the perpendicular bisector of ST. Prove that ∆MST is isosceles.
Statements Reasons
Given1.1. MN is the bisector of ST.
Now You Try
Now You Try
Page 276
Complete Page 277-278#s 10-24 & 32 even Only