bell ringer. angle bisector and perpendicular bisector
TRANSCRIPT
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Bell Ringer
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Angle Bisector and Perpendicular Bisector
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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.
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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.
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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.
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Perpendicular Bisector– Perpendicular A segment, ray, or line that is
perpendicular to a segment at its midpoint.
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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.
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Now You Try Use Angle Bisectors and Perpendicular Bisectors
ANSWER 5
ANSWER 20
ANSWER 15
1. Find FH.
2. Find MK.
3. Find EF.
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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.
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Now You Try
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Now You Try
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Complete Page 277-278#s 10-24 & 32 even Only