Sec. 52 Bisectors in s

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Sec. 5-2Bisectors in ?s

• Objectives
• 1) To use properties of ? bisectors and ?
  bisectors.

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GEOMETRY LESSON 5-2
(For help, go to Lesson 1-5.)
5-2
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Bisectors in Triangles
GEOMETRY LESSON 5-2
Solutions
5-2
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Th(5 2) ? Bisector Thm

• If a point is on the ? bisector of a segment,
  then it is equidistant from the endpoints of the
  segments.

C
?ADC ? ?BDC by SAS
CD is the ? bisector of ?ABC CD is the bisector
or AB CD is the ? bisector of ?ACB
A
B
D
Any point on CD is the same distance from Pt. A
and from Pt. B
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Th(5 3) Converse of the ? Bisector Thm

• If a point is equidistant from the endpoints of a
  segment, then it is on the ? bisector of the
  segments.

Locus Theorems A set of points that satisfy a
given condition.
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Distance from a point to a line is the length
of the ? segment from the point to the line.
P
D
B
A
The distance from P to AB is the length of PD.
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Th(5 4) ? Bisector Thm.

• If a point is on the bisector of an ?, then the
  point is equidistant from the sides of the ?.

A
?ABD ? ?CBD
D
1
The distance from D to AB is AD
2
The distance from D to BC is DC
B
?ABD ? ?CBD by AAS
C
AB ? CB and AD ? CD
?1 ? ?2
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Example 2
Find FD
C
D
B
5x
2x 24
F
FD 2x 24 2(8) 24 16 24 40
5x 2x 24 3x 24 x 8
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GEOMETRY LESSON 5-2
The Converse of the Perpendicular Bisector
Theorem states If a point is equidistant from
the endpoints of a segment, then it is on the
perpendicular bisector of the segment.
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GEOMETRY LESSON 5-2
Therefore, all points on the perpendicular
bisector of the segment whose endpoints are the
Lincoln Memorial and the Capitol are equidistant
from the Lincoln Memorial and the Capitol.
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GEOMETRY LESSON 5-2
FD FB Angle Bisector Theorem
7x 37 2x 5 Substitute.
7x 2x 42 Add 37 to each side.
5x 42 Subtract 2x from each side.
x 8.4 Divide each side by 5.
FB 2(8.4) 5 21.8 Substitute.
FD 7(8.4) 37 21.8 Substitute.
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Example 3
C
(x 20)
2x
D
B
F
Find m?BCD
2x x 20 x 20 m?BCF 2x 2(20) 40
m?BCD 2m ?BCF 2(40) 80
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GEOMETRY LESSON 5-2
Use this figure for Exercises 13. 1. Find
BD. 2. Complete the statement C is
equidistant from ? . 3. Can you conclude
that CN DN? Explain.
Use this figure for Exercises 46. 4. Find
the value of x. 5. Find CG. 6. Find the
perimeter of quadrilateral ABCG.
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16
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points A and B
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