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.

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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.

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.

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

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